text:
@book{fishman1996MonteCarloConcepts,
	address = {New York},
	series = {Springer {Series} in {Operations} {Research} and {Financial} {Engineering}},
	title = {Monte {Carlo}: {Concepts}, {Algorithms}, and {Applications}},
	isbn = {978-0-387-94527-9},
	shorttitle = {Monte {Carlo}},
	url = {https://www.springer.com/gp/book/9780387945279},
	abstract = {This book provides an introduction to the Monte Carlo method suitable for a one-or two-semester course for graduate and advanced undergraduate students in the mathematical and engineering sciences. It also can serve as a reference for the professional analyst. In the past, my inability to provide students with a single source book on this topic for class and for later professional reference had left me repeatedly frustrated, and eventually motivated me to write this book. In addition to focused accounts of major topics, the book has two unifying themes: One concerns the effective use of information and the other concerns error control and reduction. The book describes how to incorporate information about a problem into a sampling plan in a way that reduces the cost of estimating its solution to within a specified error bound. Although exploiting special structures to reduce cost long has been a hallmark of the Monte Carlo method, the propen sity of users of the method to discard useful information because it does not fit traditional textbook models repeatedly has impressed me. The present account aims at reducing the impediments to integrating this information. Errors, both statistical and computational, abound in every Monte Carlo sam pling experiment, and a considerable methodology exists for controlling them.},
	language = {en},
	urldate = {2021-09-24},
	publisher = {Springer-Verlag},
	author = {Fishman, George},
	year = {1996},
	doi = {10.1007/978-1-4757-2553-7},
	file = {Snapshot:/Users/yulei/Zotero/storage/Q3YAC3BP/9780387945279.html:text/html;全文:/Users/yulei/Zotero/storage/F3PBSQQ2/Fishman - 1996 - Monte Carlo Concepts, Algorithms, and Application.pdf:application/pdf},
}

@article{loh1996LatinHypercubeSampling,
	title = {On {Latin} {Hypercube} {Sampling}},
	volume = {24},
	issn = {0090-5364},
	url = {https://www.jstor.org/stable/2242641},
	abstract = {This paper contains a collection of results on Latin hypercube sampling. The first result is a Berry-Esseen-type bound for the multivariate central limit theorem of the sample mean μ̂n based on a Latin hypercube sample. The second establishes sufficient conditions on the convergence rate in the strong law for μ̂n. Finally motivated by the concept of empirical likelihood, a way of constructing nonparametric confidence regions based on Latin hypercube samples is proposed for vector means.},
	number = {5},
	urldate = {2021-09-24},
	journal = {The Annals of Statistics},
	author = {Loh, Wei-Liem},
	year = {1996},
	note = {Publisher: Institute of Mathematical Statistics},
	pages = {2058--2080},
}

@book{niederreiter1992RandomNumberGeneration,
	address = {USA},
	title = {Random number generation and quasi-{Monte} {Carlo} methods},
	isbn = {978-0-89871-295-7},
	publisher = {Society for Industrial and Applied Mathematics},
	author = {Niederreiter, Harald},
	year = {1992},
}

@article{bellman1966DynamicProgramming,
	title = {Dynamic {Programming}},
	volume = {153},
	issn = {0036-8075, 1095-9203},
	url = {https://www.sciencemag.org/lookup/doi/10.1126/science.153.3731.34},
	doi = {10.1126/science.153.3731.34},
	language = {en},
	number = {3731},
	urldate = {2021-09-23},
	journal = {Science},
	author = {Bellman, R.},
	month = jul,
	year = {1966},
	pages = {34--37},
	file = {全文:/Users/yulei/Zotero/storage/Z285JYNK/Bellman - 1966 - Dynamic Programming.pdf:application/pdf},
}

@article{bou-zeid2004ParametricSensitivityAnalysis,
	title = {Parametric sensitivity analysis of leachate transport simulations at landfills},
	volume = {24},
	issn = {0956-053X},
	url = {https://www.sciencedirect.com/science/article/pii/S0956053X04000571},
	doi = {10.1016/j.wasman.2004.03.004},
	abstract = {This paper presents a case study in simulating leachate generation and transport at a 2000 ton/day landfill facility and assesses leachate migration away from the landfill in order to control associated environmental impacts, particularly on groundwater wells down gradient of the site. The site offers unique characteristics in that it is a former quarry converted to a landfill and is planned to have refuse depths that could reach 100 m, making it one of the deepest in the world. Leachate quantity and potential percolation into the subsurface are estimated using the Hydrologic Evaluation of Landfill Performance (HELP) model. A three-dimensional subsurface model (PORFLOW) was adopted to simulate ground water flow and contaminant transport away from the site. A comprehensive sensitivity analysis to leachate transport control parameters was also conducted. Sensitivity analysis suggests that changes in partition coefficient, source strength, aquifer hydraulic conductivity, and dispersivity have the most significant impact on model output indicating that these parameters should be carefully selected when similar modeling studies are performed.},
	language = {en},
	number = {7},
	urldate = {2021-02-25},
	journal = {Waste Management},
	author = {Bou-Zeid, E and El-Fadel, M},
	month = jan,
	year = {2004},
	pages = {681--689},
	file = {ScienceDirect Snapshot:/Users/yulei/Zotero/storage/NWSVPGAT/S0956053X04000571.html:text/html;Bou-Zeid_El-Fadel_2004_Parametric sensitivity analysis of leachate transport simulations at landfills.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Bou-Zeid_El-Fadel_2004_Parametric sensitivity analysis of leachate transport simulations at landfills.pdf:application/pdf},
}

@article{leeComplexitiesAgentBasedModeling2015,
	title = {The {Complexities} of {Agent}-{Based} {Modeling} {Output} {Analysis}},
	volume = {18},
	issn = {1460-7425},
	doi = {10.18564/jasss.2897},
	number = {4},
	journal = {Journal of Artificial Societies and Social Simulation},
	author = {Lee, Ju-Sung and Filatova, Tatiana and Ligmann-Zielinska, Arika and Hassani-Mahmooei, Behrooz and Stonedahl, Forrest and Lorscheid, Iris and Voinov, Alexey and Polhill, J. Gary and Sun, Zhanli and Parker, Dawn C.},
	year = {2015},
	pages = {4},
	file = {Lee 等。 - 2015 - The Complexities of Agent-Based Modeling Output An.pdf:/Users/yulei/Zotero/storage/J97B8JI8/Lee 等。 - 2015 - The Complexities of Agent-Based Modeling Output An.pdf:application/pdf;The Complexities of Agent-Based Modeling Output Analysis:/Users/yulei/Zotero/storage/ZBNTKFKL/4.html:text/html},
}

@article{campolongo1997SensitivityAnalysisEnvironmental,
	series = {The {Role} of {Sensitivity} {Analysis} in the {Corroboration} of {Models} and its {Links} to {Model} {Structural} and {Parametric} {Uncertainty}},
	title = {Sensitivity analysis of an environmental model: an application of different analysis methods},
	volume = {57},
	issn = {0951-8320},
	shorttitle = {Sensitivity analysis of an environmental model},
	url = {https://www.sciencedirect.com/science/article/pii/S0951832097000215},
	doi = {10.1016/S0951-8320(97)00021-5},
	abstract = {A parametric sensitivity analysis (SA) was conducted on a well known model for the production of a key sulphur bearing compound from algal biota. The model is of interest because of the climatic relevance of the gas (dimethylsulphide, DMS), an initiator of cloud particles. A screening test at low sample size is applied first (Morris method) followed by a computationally intensive variance based measure. Standardised regression coefficients are also computed. The various SA measures are compared with each other, and the use of bootstrap is suggested to extract empirical confidence bounds on the SA estimators. For some of the input factors, investigators guess about the parameters relevance was confirmed; for some others, the results shed new light on the system mechanism and on the data parametrisation.},
	language = {en},
	number = {1},
	urldate = {2021-02-24},
	journal = {Reliability Engineering \& System Safety},
	author = {Campolongo, Francesca and Saltelli, Andrea},
	month = jul,
	year = {1997},
	pages = {49--69},
	file = {ScienceDirect Snapshot:/Users/yulei/Zotero/storage/CTIQE7WD/S0951832097000215.html:text/html;Campolongo_Saltelli_1997_Sensitivity analysis of an environmental model.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Campolongo_Saltelli_1997_Sensitivity analysis of an environmental model.pdf:application/pdf},
}

@article{geComprehensiveApproachSensitivity2014,
	title = {Comprehensive {Approach} for the {Sensitivity} {Analysis} of {High}-{Dimensional} and {Computationally} {Expensive} {Traffic} {Simulation} {Models}},
	volume = {2422},
	issn = {0361-1981},
	url = {https://doi.org/10.3141/2422-14},
	doi = {10.3141/2422-14},
	abstract = {The reliability of traffic model results is strictly connected to the quality of its calibration. A challenge arising in this context concerns the selection of the most influential input parameters. A model sensitivity analysis should be used with this aim. However, because of the limitations of time and computational resources, a proper sensitivity analysis is rarely performed in common practice. A recent study introduced a methodology based on Gaussian process metamodels for the sensitivity analysis of computationally expensive traffic simulation models. The main limitation was a dependence on model dimensionality. When the model has more than about 15 to 20 parameters, estimation of a Gaussian process metamodel (also known as a Kriging metamodel) may become problematic. In this paper, the Kriging-based approach is coupled with a recently developed approach, quasi-optimized trajectory-based elementary effects (quasi-OTEE), for the sensitivity analysis of computationally expensive models. The quasi-OTEE sensitivity analysis can be used to identify the whole subset of sensitive parameters of a high-dimensional model, and the Kriging-based sensitivity analysis can then be used to refine the analysis and to rank the different parameters of the subset in a more reliable way. Application of this new sequential sensitivity analysis method is illustrated with the Wiedemann-74 car-following model. Results show that the new method requires 40 times fewer model evaluations than a standard variance-based sensitivity analysis to identify the influential parameters and their ranks.},
	language = {en},
	number = {1},
	urldate = {2021-02-24},
	journal = {Transportation Research Record},
	author = {Ge, Qiao and Ciuffo, Biagio and Menendez, Monica},
	month = jan,
	year = {2014},
	note = {Publisher: SAGE Publications Inc},
	pages = {121--130},
	file = {Ge 等。 - 2014 - Comprehensive Approach for the Sensitivity Analysi.pdf:/Users/yulei/Zotero/storage/NWPBKWE9/Ge 等。 - 2014 - Comprehensive Approach for the Sensitivity Analysi.pdf:application/pdf},
}

@article{ge2014EfficientSensitivityAnalysis,
	title = {An {Efficient} {Sensitivity} {Analysis} {Approach} for {Computationally} {Expensive} {Microscopic} {Traffic} {Simulation} {Models}},
	volume = {2},
	issn = {2287-7940},
	url = {https://trid.trb.org/view/1407674},
	number = {2},
	urldate = {2021-02-24},
	journal = {International Journal of Transportation},
	author = {Ge, Qiao and Menendez, Monica},
	year = {2014},
	file = {Snapshot:/Users/yulei/Zotero/storage/UZCU2E5W/1407674.html:text/html;Ge_Menendez_2014_An Efficient Sensitivity Analysis Approach for Computationally Expensive.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Ge_Menendez_2014_An Efficient Sensitivity Analysis Approach for Computationally Expensive.pdf:application/pdf},
}

@misc{SensitivityAnalysisPractice,
	title = {Sensitivity {Analysis} in {Practice}: {A} {Guide} to {Assessing} {Scientific} {Models} {\textbar} {Wiley}},
	shorttitle = {Sensitivity {Analysis} in {Practice}},
	url = {https://www.wiley.com/en-us/Sensitivity+Analysis+in+Practice%3A+A+Guide+to+Assessing+Scientific+Models-p-9780470870938},
	abstract = {Sensitivity analysis should be considered a pre-requisite for statistical model building in any scientific discipline where modelling takes place. For a non-expert, choosing the method of analysis for their model is complex, and depends on a number of factors. This book guides the non-expert through their problem in order to enable them to choose and apply the most appropriate method. It offers a review of the state-of-the-art in sensitivity analysis, and is suitable for a wide range of practitioners. It is focussed on the use of SIMLAB – a widely distributed freely-available sensitivity analysis software package developed by the authors – for solving problems in sensitivity analysis of statistical models. Other key features: Provides an accessible overview of the current most widely used methods for sensitivity analysis. Opens with a detailed worked example to explain the motivation behind the book. Includes a range of examples to help illustrate the concepts discussed. Focuses on implementation of the methods in the software SIMLAB - a freely-available sensitivity analysis software package developed by the authors. Contains a large number of references to sources for further reading. Authored by the leading authorities on sensitivity analysis.},
	language = {en-us},
	urldate = {2021-02-22},
	journal = {Wiley.com},
	file = {Snapshot:/Users/yulei/Zotero/storage/LEJ35SXN/Sensitivity+Analysis+in+Practice+A+Guide+to+Assessing+Scientific+Models-p-9780470870938.html:text/html;Sensitivity Analysis in Practice.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Sensitivity Analysis in Practice.pdf:application/pdf},
}

@misc{2010GlobalSensitivityAnalysis,
	title = {Global {Sensitivity} {Analysis}: {The} {Primer}},
	shorttitle = {Global {Sensitivity} {Analysis}},
	url = {https://www.wiley.com/en-us/Global+Sensitivity+Analysis%3A+The+Primer-p-9780470059975},
	abstract = {Complex mathematical and computational models are used in all areas of society and technology and yet model based science is increasingly contested or refuted, especially when models are applied to controversial themes in domains such as health, the environment or the economy. More stringent standards of proofs are demanded from model-based numbers, especially when these numbers represent potential financial losses, threats to human health or the state of the environment. Quantitative sensitivity analysis is generally agreed to be one such standard. Mathematical models are good at mapping assumptions into inferences. A modeller makes assumptions about laws pertaining to the system, about its status and a plethora of other, often arcane, system variables and internal model settings. To what extent can we rely on the model-based inference when most of these assumptions are fraught with uncertainties? Global Sensitivity Analysis offers an accessible treatment of such problems via quantitative sensitivity analysis, beginning with the first principles and guiding the reader through the full range of recommended practices with a rich set of solved exercises. The text explains the motivation for sensitivity analysis, reviews the required statistical concepts, and provides a guide to potential applications. The book: Provides a self-contained treatment of the subject, allowing readers to learn and practice global sensitivity analysis without further materials. Presents ways to frame the analysis, interpret its results, and avoid potential pitfalls. Features numerous exercises and solved problems to help illustrate the applications. Is authored by leading sensitivity analysis practitioners, combining a range of disciplinary backgrounds. Postgraduate students and practitioners in a wide range of subjects, including statistics, mathematics, engineering, physics, chemistry, environmental sciences, biology, toxicology, actuarial sciences, and econometrics will find much of use here. This book will prove equally valuable to engineers working on risk analysis and to financial analysts concerned with pricing and hedging.},
	language = {en-us},
	urldate = {2021-02-15},
	journal = {Wiley.com},
	year = {2010},
	file = {Global Sensitivity Analysis The Primer  Wiley.pdf:/Users/yulei/Zotero/storage/AXXP6CEI/Global Sensitivity Analysis The Primer  Wiley.pdf:application/pdf;Snapshot:/Users/yulei/Zotero/storage/U9Q39CX6/Global+Sensitivity+Analysis+The+Primer-p-9780470059975.html:text/html},
}

@article{liebermanGoalOrientedInferenceApproach2013,
	title = {Goal-{Oriented} {Inference}: {Approach}, {Linear} {Theory}, and {Application} to {Advection} {Diffusion}},
	shorttitle = {Goal-{Oriented} {Inference}},
	doi = {10.1137/130913110},
	abstract = {Inference of model parameters is one step in an engineering process often ending in predictions that support decision in the form of design or control. Incorporation of end goals into the inference process leads to more efficient goal-oriented algorithms that automatically target the most relevant parameters for prediction. In the linear setting the control-theoretic concepts underlying balanced truncation model reduction can be exploited in inference through a dimensionally optimal subspace regularizer. The inference-for-prediction method exactly replicates the prediction results of either truncated singular value decomposition, Tikhonov-regularized, or Gaussian statistical inverse problem formulations independent of data; it sacrifices accuracy in parameter estimate for online efficiency. The new method leads to low-dimensional parameterization of the inverse problem enabling solution on smartphones or laptops in the field.},
	journal = {SIAM Rev.},
	author = {Lieberman, Chad and Willcox, K.},
	year = {2013},
	file = {Full Text PDF:/Users/yulei/Zotero/storage/WV9WHDA8/Lieberman 和 Willcox - 2013 - Goal-Oriented Inference Approach, Linear Theory, .pdf:application/pdf},
}

@article{liebermanNonlinearGoalOrientedBayesian2014,
	title = {Nonlinear {Goal}-{Oriented} {Bayesian} {Inference}: {Application} to {Carbon} {Capture} and {Storage}},
	volume = {36},
	issn = {1064-8275},
	shorttitle = {Nonlinear {Goal}-{Oriented} {Bayesian} {Inference}},
	url = {https://epubs.siam.org/doi/10.1137/130928315},
	doi = {10.1137/130928315},
	abstract = {In many engineering problems, unknown parameters of a model are inferred in order to make predictions, to design controllers, or to  optimize the model.  When parameters are distributed (continuous) or very high-dimensional (discrete) and quantities of interest are low-dimensional, parameters need not be fully resolved to make accurate estimates of quantities of interest. In this work, we extend goal-oriented inference---the process of estimating predictions from observed data without resolving the parameter, previously justified theoretically in the linear setting---to Bayesian statistical inference problem formulations with nonlinear experimental and prediction processes. We propose to learn the joint density of data and predictions offline using Gaussian mixture models. When data are observed online, we condition the representation to arrive at a probabilistic description of predictions given observed data.  Our approach enables real-time estimation of uncertainty in quantities of interest and renders tractable high-dimensional PDE-constrained Bayesian inference when there exist low-dimensional output quantities of interest.  We demonstrate the method on a realistic problem in carbon capture and storage for which existing methods of Bayesian parameter estimation are intractable.},
	number = {3},
	urldate = {2021-02-10},
	journal = {SIAM Journal on Scientific Computing},
	author = {Lieberman, Chad and Willcox, Karen},
	month = jan,
	year = {2014},
	note = {Publisher: Society for Industrial and Applied Mathematics},
	pages = {B427--B449},
	file = {全文:/Users/yulei/Zotero/storage/PZ7LT2YY/Lieberman 和 Willcox - 2014 - Nonlinear Goal-Oriented Bayesian Inference Applic.pdf:application/pdf;Snapshot:/Users/yulei/Zotero/storage/22SH2PTM/130928315.html:text/html},
}

@article{borgonovo2016CommonRationaleGlobal,
	title = {A {Common} {Rationale} for {Global} {Sensitivity} {Measures} and {Their} {Estimation}},
	volume = {36},
	issn = {1539-6924},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.1111/risa.12555},
	doi = {10.1111/risa.12555},
	abstract = {Measures of sensitivity and uncertainty have become an integral part of risk analysis. Many such measures have a conditional probabilistic structure, for which a straightforward Monte Carlo estimation procedure has a double-loop form. Recently, a more efficient single-loop procedure has been introduced, and consistency of this procedure has been demonstrated separately for particular measures, such as those based on variance, density, and information value. In this work, we give a unified proof of single-loop consistency that applies to any measure satisfying a common rationale. This proof is not only more general but invokes less restrictive assumptions than heretofore in the literature, allowing for the presence of correlations among model inputs and of categorical variables. We examine numerical convergence of such an estimator under a variety of sensitivity measures. We also examine its application to a published medical case study.},
	language = {en},
	number = {10},
	urldate = {2021-02-10},
	journal = {Risk Analysis},
	author = {Borgonovo, Emanuele and Hazen, Gordon B. and Plischke, Elmar},
	year = {2016},
	note = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1111/risa.12555},
	keywords = {Global sensitivity measures, Monte Carlo simulation, probabilistic sensitivity analysis, risk analysis, uncertainty analysis},
	pages = {1871--1895},
	file = {Borgonovo 等。 - 2016 - A Common Rationale for Global Sensitivity Measures.pdf:/Users/yulei/Zotero/storage/6RBVWID9/Borgonovo 等。 - 2016 - A Common Rationale for Global Sensitivity Measures.pdf:application/pdf;Snapshot:/Users/yulei/Zotero/storage/C8QA5N32/risa.html:text/html;Borgonovo et al_2016_A Common Rationale for Global Sensitivity Measures and Their Estimation.txt:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Borgonovo et al_2016_A Common Rationale for Global Sensitivity Measures and Their Estimation.txt:text/plain},
}

@article{razavi2021FutureSensitivityAnalysis,
	title = {The {Future} of {Sensitivity} {Analysis}: {An} essential discipline for systems modeling and policy support},
	volume = {137},
	issn = {1364-8152},
	shorttitle = {The {Future} of {Sensitivity} {Analysis}},
	url = {http://www.sciencedirect.com/science/article/pii/S1364815220310112},
	doi = {10.1016/j.envsoft.2020.104954},
	abstract = {Sensitivity analysis (SA) is en route to becoming an integral part of mathematical modeling. The tremendous potential benefits of SA are, however, yet to be fully realized, both for advancing mechanistic and data-driven modeling of human and natural systems, and in support of decision making. In this perspective paper, a multidisciplinary group of researchers and practitioners revisit the current status of SA, and outline research challenges in regard to both theoretical frameworks and their applications to solve real-world problems. Six areas are discussed that warrant further attention, including (1) structuring and standardizing SA as a discipline, (2) realizing the untapped potential of SA for systems modeling, (3) addressing the computational burden of SA, (4) progressing SA in the context of machine learning, (5) clarifying the relationship and role of SA to uncertainty quantification, and (6) evolving the use of SA in support of decision making. An outlook for the future of SA is provided that underlines how SA must underpin a wide variety of activities to better serve science and society.},
	language = {en},
	urldate = {2021-02-03},
	journal = {Environmental Modelling \& Software},
	author = {Razavi, Saman and Jakeman, Anthony and Saltelli, Andrea and Prieur, Clémentine and Iooss, Bertrand and Borgonovo, Emanuele and Plischke, Elmar and Lo Piano, Samuele and Iwanaga, Takuya and Becker, William and Tarantola, Stefano and Guillaume, Joseph H. A. and Jakeman, John and Gupta, Hoshin and Melillo, Nicola and Rabitti, Giovanni and Chabridon, Vincent and Duan, Qingyun and Sun, Xifu and Smith, Stefán and Sheikholeslami, Razi and Hosseini, Nasim and Asadzadeh, Masoud and Puy, Arnald and Kucherenko, Sergei and Maier, Holger R.},
	month = mar,
	year = {2021},
	keywords = {Decision making, Machine learning, Mathematical modeling, Model robustness, Model validation and verification, Policy support, Sensitivity analysis, Uncertainty quantification},
	pages = {104954},
	file = {ScienceDirect Snapshot:/Users/yulei/Zotero/storage/CJ34XNZ3/S1364815220310112.html:text/html;Razavi et al_2021_The Future of Sensitivity Analysis.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Razavi et al_2021_The Future of Sensitivity Analysis.pdf:application/pdf},
}

@article{krinsky1986ApproximatingStatisticalProperties,
	title = {On {Approximating} the {Statistical} {Properties} of {Elasticities}},
	volume = {68},
	issn = {0034-6535},
	url = {https://www.jstor.org/stable/1924536},
	doi = {10.2307/1924536},
	abstract = {This paper argues for the use of a simulation methodology to examine the distributions of elasticities that, in turn, are complex, non-linear functions of estimated parameters. Linear approximations are often used in this context but are shown to be poor substitutes for the suggested procedure.},
	number = {4},
	urldate = {2021-01-15},
	journal = {The Review of Economics and Statistics},
	author = {Krinsky, Itzhak and Robb, A. Leslie},
	year = {1986},
	note = {Publisher: The MIT Press},
	pages = {715--719},
	file = {Krinsky_Robb_1986_On Approximating the Statistical Properties of Elasticities.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Krinsky_Robb_1986_On Approximating the Statistical Properties of Elasticities.pdf:application/pdf},
}

@article{keane1997CareerDecisionsYoung,
	title = {The {Career} {Decisions} of {Young} {Men}},
	volume = {105},
	issn = {0022-3808},
	url = {https://www.jstor.org/stable/10.1086/262080},
	doi = {10.1086/262080},
	abstract = {This paper provides structural estimates of a dynamic model of schooling, work, and occupational choice decisions based on 11 years of observations on a sample of young men from the 1979 youth cohort of the National Longitudinal Surveys of Labor Market Experience (NLSY). The structural estimation framework that we adopt fully imposes the restrictions of the theory and permits an investigation of whether such a theoretically restricted model can succeed in quantitatively fitting the observed data patterns. We find that a suitably extended human capital investment model can in fact do an excellent job of fitting observed data on school attendance, work, occupational choices, and wages in the NLSY data on young men and also produces reasonable forecasts of future work decisions and wage patterns.},
	number = {3},
	urldate = {2020-12-17},
	journal = {Journal of Political Economy},
	author = {Keane, Michael P. and Wolpin, Kenneth I.},
	year = {1997},
	note = {Publisher: The University of Chicago Press},
	pages = {473--522},
	file = {Keane_Wolpin_1997_The Career Decisions of Young Men.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Keane_Wolpin_1997_The Career Decisions of Young Men.pdf:application/pdf},
}

@article{keane1994SolutionEstimationDiscrete,
	title = {The {Solution} and {Estimation} of {Discrete} {Choice} {Dynamic} {Programming} {Models} by {Simulation} and {Interpolation}: {Monte} {Carlo} {Evidence}},
	volume = {76},
	issn = {0034-6535},
	shorttitle = {The {Solution} and {Estimation} of {Discrete} {Choice} {Dynamic} {Programming} {Models} by {Simulation} and {Interpolation}},
	url = {https://www.jstor.org/stable/2109768},
	doi = {10.2307/2109768},
	abstract = {Over the past decade, a substantial literature on methods for the estimation of discrete choice dynamic programming (DDP) models of behavior has developed. However, the implementation of these methods can impose major computational burdens because solving for agents' decision rules often involves high dimensional integrations that must be performed at each point in the state space. In this paper we develop an approximate solution method that consists of: 1) using Monte Carlo integration to stimulate the required multiple integrals at a subset of the state points, and 2) interpolating the non-simulated values using a regression function. The overall performance of this approximation method appears to be excellent.},
	number = {4},
	urldate = {2020-12-04},
	journal = {The Review of Economics and Statistics},
	author = {Keane, Michael P. and Wolpin, Kenneth I.},
	year = {1994},
	note = {Publisher: The MIT Press},
	pages = {648--672},
	file = {Keane_Wolpin_1994_The Solution and Estimation of Discrete Choice Dynamic Programming Models by.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Keane_Wolpin_1994_The Solution and Estimation of Discrete Choice Dynamic Programming Models by.pdf:application/pdf},
}

@article{kala2019QuantileorientedGlobalSensitivity,
	title = {Quantile-oriented global sensitivity analysis of design resistance},
	volume = {25},
	copyright = {Copyright (c) 2019 The Author(s). Published by VGTU Press.},
	issn = {1822-3605},
	url = {https://journals.vgtu.lt/index.php/JCEM/article/view/9627},
	doi = {10.3846/jcem.2019.9627},
	abstract = {The article investigates the application of a new type of global quantile-oriented sensitivity analysis (called QSA in the article) and contrasts it with established Sobol’ sensitivity analysis (SSA). Comparison of QSA of the resistance design value (0.1 percentile) with SSA is performed on an example of the analysis of the resistance of a steel IPN 200 beam, which is subjected to lateral-torsional buckling. The resistance is approximated using higher order polynomial metamodels created from advanced non-linear FE models. The main, higher order and total effects are calculated using the Latin Hypercube Sampling method. Noticeable differences between the two methods are found, with QSA apparently revealing higher sensitivity of the resistance design value to random input second and higher order interactions (compared to SSA). SSA cannot identify certain reliability aspects of structural design as comprehensively as QSA, particularly in relation to higher order interactions effects of input imperfections. In order to better understand the reasons for the differences between QSA and SSA, two simple examples are presented, where QSA (median) and SSA show a general agreement in the calculation of certain sensitivity indices.
													Keyword :
																											sensitivity analysis,
																			quantile,
																			resistance,
																			lateral-torsional buckling,
																			imperfections,
																			steel,
																			random sampling

								How to Cite

  Kala, Z. (2019). Quantile-oriented global sensitivity analysis of design resistance. Journal of Civil Engineering and Management, 25(4), 297-305. https://doi.org/10.3846/jcem.2019.9627

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	language = {en},
	number = {4},
	urldate = {2020-09-10},
	journal = {Journal of Civil Engineering and Management},
	author = {Kala, Zdeněk},
	month = apr,
	year = {2019},
	note = {Number: 4},
	keywords = {imperfections, lateral-torsional buckling, quantile, random sampling, resistance, sensitivity analysis, steel},
	pages = {297--305},
	file = {Snapshot:/Users/yulei/Zotero/storage/RSDL6K8G/9627.html:text/html;Kala_2019_Quantile-oriented global sensitivity analysis of design resistance.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Kala_2019_Quantile-oriented global sensitivity analysis of design resistance.pdf:application/pdf},
}

@article{kucherenko2017DifferentNumericalEstimators,
	title = {Different numerical estimators for main effect global sensitivity indices},
	volume = {165},
	issn = {0951-8320},
	url = {http://www.sciencedirect.com/science/article/pii/S0951832016301065},
	doi = {10.1016/j.ress.2017.04.003},
	abstract = {The variance-based method of global sensitivity indices based on Sobol' sensitivity indices became very popular among practitioners due to its easiness of interpretation. For complex practical problems computation of Sobol' indices generally requires a large number of function evaluations to achieve reasonable convergence. Four different direct formulas for computing Sobol’ main effect sensitivity indices are compared on a set of test models for which there are analytical results. Considered test functions represent various types of models that are found in practice. Formulas are based on high-dimensional integrals which are evaluated using Monte Carlo (MC) and Quasi Monte Carlo (QMC) techniques. Direct formulas are also compared with a different approach based on the so-called “double loop reordering” formula. It is found that the “double loop reordering” (DLR) approach shows a superior performance among all methods both for models with independent and dependent variables.},
	language = {en},
	urldate = {2020-08-30},
	journal = {Reliability Engineering \& System Safety},
	author = {Kucherenko, S. and Song, S.},
	month = sep,
	year = {2017},
	keywords = {Double loop reordering, Global sensitivity analysis, Quasi Monte Carlo, Sobol’ sensitivity indices},
	pages = {222--238},
	file = {ScienceDirect Snapshot:/Users/yulei/Zotero/storage/P2N985EY/S0951832016301065.html:text/html;Kucherenko_Song_2017_Different numerical estimators for main effect global sensitivity indices.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Kucherenko_Song_2017_Different numerical estimators for main effect global sensitivity indices.pdf:application/pdf;Kucherenko_Song_2017_Different numerical estimators for main effect global sensitivity indices.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Kucherenko_Song_2017_Different numerical estimators for main effect global sensitivity indices2.pdf:application/pdf},
}

@article{kucherenko2012EstimationGlobalSensitivity,
	title = {Estimation of global sensitivity indices for models with dependent variables},
	volume = {183},
	issn = {0010-4655},
	url = {http://www.sciencedirect.com/science/article/pii/S0010465511004085},
	doi = {10.1016/j.cpc.2011.12.020},
	abstract = {A novel approach for estimation variance-based sensitivity indices for models with dependent variables is presented. Both the first order and total sensitivity indices are derived as generalizations of Sobolʼ sensitivity indices. Formulas and Monte Carlo numerical estimates similar to Sobolʼ formulas are derived. A copula-based approach is proposed for sampling from arbitrary multivariate probability distributions. A good agreement between analytical and numerical values of the first order and total indices for considered test cases is obtained. The behavior of sensitivity indices depends on the relative predominance of interactions and correlations. The method is shown to be efficient and general.},
	language = {en},
	number = {4},
	urldate = {2020-08-20},
	journal = {Computer Physics Communications},
	author = {Kucherenko, S. and Tarantola, S. and Annoni, P.},
	month = apr,
	year = {2012},
	keywords = {Global sensitivity analysis, Correlated inputs, Gaussian copula, Quasi Monte Carlo methods, Sobolʼ sensitivity indices, Sobolʼ sequences},
	pages = {937--946},
	file = {ScienceDirect Snapshot:/Users/yulei/Zotero/storage/HCNZVZ8G/S0010465511004085.html:text/html;Kucherenko et al_2012_Estimation of global sensitivity indices for models with dependent variables.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Kucherenko et al_2012_Estimation of global sensitivity indices for models with dependent variables.pdf:application/pdf},
}

@article{borgonovo2016SensitivityAnalysisReview,
	title = {Sensitivity analysis: {A} review of recent advances},
	volume = {248},
	issn = {0377-2217},
	shorttitle = {Sensitivity analysis},
	url = {http://www.sciencedirect.com/science/article/pii/S0377221715005469},
	doi = {10.1016/j.ejor.2015.06.032},
	abstract = {The solution of several operations research problems requires the creation of a quantitative model. Sensitivity analysis is a crucial step in the model building and result communication process. Through sensitivity analysis we gain essential insights on model behavior, on its structure and on its response to changes in the model inputs. Several interrogations are possible and several sensitivity analysis methods have been developed, giving rise to a vast and growing literature. We present an overview of available methods, structuring them into local and global methods. For local methods, we discuss Tornado diagrams, one way sensitivity functions, differentiation-based methods and scenario decomposition through finite change sensitivity indices, providing a unified view of the associated sensitivity measures. We then analyze global sensitivity methods, first discussing screening methods such as sequential bifurcation and the Morris method. We then address variance-based, moment-independent and value of information-based sensitivity methods. We discuss their formalization in a common rationale and present recent results that permit the estimation of global sensitivity measures by post-processing the sample generated by a traditional Monte Carlo simulation. We then investigate in detail the methodological issues concerning the crucial step of correctly interpreting the results of a sensitivity analysis. A classical example is worked out to illustrate some of the approaches.},
	language = {en},
	number = {3},
	urldate = {2020-08-17},
	journal = {European Journal of Operational Research},
	author = {Borgonovo, Emanuele and Plischke, Elmar},
	month = feb,
	year = {2016},
	keywords = {Sensitivity analysis, Computer experiments, Simulation},
	pages = {869--887},
	file = {ScienceDirect Snapshot:/Users/yulei/Zotero/storage/AD9XFENC/S0377221715005469.html:text/html;Borgonovo_Plischke_2016_Sensitivity analysis.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Borgonovo_Plischke_2016_Sensitivity analysis.pdf:application/pdf},
}

@article{luyi2012MomentindependentImportanceMeasure,
	title = {Moment-independent importance measure of basic variable and its state dependent parameter solution},
	volume = {38},
	issn = {0167-4730},
	url = {http://www.sciencedirect.com/science/article/pii/S0167473012000276},
	doi = {10.1016/j.strusafe.2012.04.001},
	abstract = {To analyze the effect of basic variable on output of the structure or system in reliability engineering, two moment-independent importance measures of the basic variable are proposed respectively on the failure probability and distribution function of the output. The importance measures proposed not only inherit the advantages of the traditional moment-independent importance measures, but also reflect the intrinsic relationship of the moment-independent measures and the corresponding variance-based importance measures. For the problem that the computational effort of the moment-independent importance measure is usually too high, the computation of the proposed moment-independent importance measures is transformed into that of the variance-based importance measures on their intrinsic relationship. And then combining the high efficient state dependent parameter (SDP) method for the calculation of the conditional moments of the model output, a SDP solution is established to solve two moment-independent importance measures. Several examples are used to demonstrate that the proposed importance measures can effectively describe the effect of the basic variable on the reliability of the structure system, and the established solution can obtain the two importance measures simultaneously with only a single set of model runs, which allows for a strong reduction of the computational cost.},
	language = {en},
	urldate = {2020-07-21},
	journal = {Structural Safety},
	author = {Luyi, Li and Zhenzhou, Lu and Jun, Feng and Bintuan, Wang},
	month = sep,
	year = {2012},
	keywords = {Basic variable, Importance measure, Moment-independent, State dependent parameter (SDP)},
	pages = {40--47},
	file = {ScienceDirect Snapshot:/Users/yulei/Zotero/storage/RI7D5IJ7/S0167473012000276.html:text/html;Luyi et al_2012_Moment-independent importance measure of basic variable and its state dependent.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Luyi et al_2012_Moment-independent importance measure of basic variable and its state dependent.pdf:application/pdf},
}

@article{yun2018EfficientGlobalReliability,
	title = {An efficient global reliability sensitivity analysis algorithm based on classification of model output and subset simulation},
	volume = {74},
	issn = {0167-4730},
	url = {http://www.sciencedirect.com/science/article/pii/S016747301730437X},
	doi = {10.1016/j.strusafe.2018.04.003},
	abstract = {The global reliability sensitivity analysis measures the effect of each model input variable on the failure probability, which is very useful for reliability-based optimization design. The aim of this paper is to propose an alternative method to estimate the global reliability sensitivity indices by one group of model input–output samples. Firstly, Bayes formula is used to convert the original expression of global reliability sensitivity index into an equivalent form where only the unconditional failure probability and the failure-conditional probability density function (PDF) of each model input variable are required. All global reliability sensitivity indices can be simultaneously estimated by this new equivalent form, and the computational cost of the process is independent of the dimensionality of model input variables. Secondly, to improve the efficiency of sampling which aims at calculating the unconditional failure probability and estimating the failure-conditional PDF of every model input simultaneously, subset simulation method is extended to achieve these two aims. In the proposed procedure, subset simulation is used to estimate the unconditional failure probability, and Metropolis-Hastings algorithm is employed to convert the samples in failure domain from the current PDF in subset simulation to the PDF corresponding to the original PDF of model inputs for estimating the failure-conditional PDF of each model input variable. Thirdly, Edgeworth expansion is employed to approximate the failure-conditional PDF of each model input variable. Finally, the global reliability sensitivity index can be easily computed as byproducts using the unconditional failure probability and the failure-conditional PDF of each model input in failure probability analysis, and this process does not need any extra model evaluations after the unconditional failure probability analysis is completed by subset simulation. A headless rivet model, a roof truss structure and a composite cantilever beam structure are analyzed, and the results demonstrate the effectiveness of the proposed method in global reliability sensitivity analysis.},
	language = {en},
	urldate = {2020-07-21},
	journal = {Structural Safety},
	author = {Yun, Wanying and Lu, Zhenzhou and Zhang, Yu and Jiang, Xian},
	month = sep,
	year = {2018},
	keywords = {Bayes formula, Dimensional-independency, Edgeworth expansion, First four-order conditional moments, Global reliability sensitivity analysis, Metropolis-Hastings algorithm},
	pages = {49--57},
	file = {ScienceDirect Snapshot:/Users/yulei/Zotero/storage/QVA5V87B/S016747301730437X.html:text/html;Yun et al_2018_An efficient global reliability sensitivity analysis algorithm based on.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Yun et al_2018_An efficient global reliability sensitivity analysis algorithm based on.pdf:application/pdf},
}

@article{borgonovo2007NewUncertaintyImportance,
	title = {A new uncertainty importance measure},
	volume = {92},
	issn = {0951-8320},
	url = {http://www.sciencedirect.com/science/article/pii/S0951832006000883},
	doi = {10.1016/j.ress.2006.04.015},
	abstract = {Uncertainty in parameters is present in many risk assessment problems and leads to uncertainty in model predictions. In this work, we introduce a global sensitivity indicator which looks at the influence of input uncertainty on the entire output distribution without reference to a specific moment of the output (moment independence) and which can be defined also in the presence of correlations among the parameters. We discuss its mathematical properties and highlight the differences between the present indicator, variance-based uncertainty importance measures and a moment independent sensitivity indicator previously introduced in the literature. Numerical results are discussed with application to the probabilistic risk assessment model on which Iman [A matrix-based approach to uncertainty and sensitivity analysis for fault trees. Risk Anal 1987;7(1):22–33] first introduced uncertainty importance measures.},
	language = {en},
	number = {6},
	urldate = {2020-07-21},
	journal = {Reliability Engineering \& System Safety},
	author = {Borgonovo, E.},
	month = jun,
	year = {2007},
	keywords = {Global sensitivity analysis, Importance measures, Probabilistic risk assessment, Uncertainty analysis, Uncertainty importance measures},
	pages = {771--784},
	file = {ScienceDirect Snapshot:/Users/yulei/Zotero/storage/B5LQ9LRA/S0951832006000883.html:text/html;Borgonovo_2007_A new uncertainty importance measure.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Borgonovo_2007_A new uncertainty importance measure.pdf:application/pdf},
}

@article{chun2000UncertaintyImportanceMeasure,
	title = {An uncertainty importance measure using a distance metric for the change in a cumulative distribution function},
	volume = {70},
	issn = {0951-8320},
	url = {http://www.sciencedirect.com/science/article/pii/S0951832000000685},
	doi = {10.1016/S0951-8320(00)00068-5},
	abstract = {A simple measure of uncertainty importance using the entire change of cumulative distribution functions (CDFs) has been developed for use in probability safety assessments (PSAs). The entire change of CDFs is quantified in terms of the metric distance between two CDFs. The metric distance measure developed in this study reflects the relative impact of distributional changes of inputs on the change of an output distribution, while most of the existing uncertainty importance measures reflect the magnitude of relative contribution of input uncertainties to the output uncertainty. The present measure has been evaluated analytically for various analytical distributions to examine its characteristics. To illustrate the applicability and strength of the present measure, two examples are provided. The first example is an application of the present measure to a typical problem of a system fault tree analysis and the second one is for a hypothetical non-linear model. Comparisons of the present result with those obtained by existing uncertainty importance measures show that the metric distance measure is a useful tool to express the measure of uncertainty importance in terms of the relative impact of distributional changes of inputs on the change of an output distribution.},
	language = {en},
	number = {3},
	urldate = {2020-07-21},
	journal = {Reliability Engineering \& System Safety},
	author = {Chun, Moon-Hyun and Han, Seok-Jung and Tak, Nam-IL},
	month = dec,
	year = {2000},
	keywords = {Importance measure, Uncertainty analysis, Metric distance, Uncertainty importance},
	pages = {313--321},
	file = {ScienceDirect Snapshot:/Users/yulei/Zotero/storage/FVHUVGSD/S0951832000000685.html:text/html;Chun et al_2000_An uncertainty importance measure using a distance metric for the change in a.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Chun et al_2000_An uncertainty importance measure using a distance metric for the change in a.pdf:application/pdf},
}

@article{hommaImportanceMeasuresGlobal1996,
	title = {Importance measures in global sensitivity analysis of nonlinear models},
	volume = {52},
	issn = {0951-8320},
	url = {http://www.sciencedirect.com/science/article/pii/0951832096000026},
	doi = {10.1016/0951-8320(96)00002-6},
	abstract = {The present paper deals with a new method of global sensitivity analysis of nonlinear models. This is based on a measure of importance to calculate the fractional contribution of the input parameters to the variance of the model prediction. Measures of importance in sensitivity analysis have been suggested by several authors, whose work is reviewed in this article. More emphasis is given to the developments of sensitivity indices by the Russian mathematician I.M. Sobol'. Given that Sobol' treatment of the measure of importance is the most general, his formalism is employed throughout this paper where conceptual and computational improvements of the method are presented. The computational novelty of this study is the introduction of the ‘total effect’ parameter index. This index provides a measure of the total effect of a given parameter, including all the possible synergetic terms between that parameter and all the others. Rank transformation of the data is also introduced in order to increase the reproducibility of the method. These methods are tested on a few analytical and computer models. The main conclusion of this work is the identification of a sensitivity analysis methodology which is both flexible, accurate and informative, and which can be achieved at reasonable computational cost.},
	language = {en},
	number = {1},
	urldate = {2020-07-18},
	journal = {Reliability Engineering \& System Safety},
	author = {Homma, Toshimitsu and Saltelli, Andrea},
	month = apr,
	year = {1996},
	pages = {1--17},
	file = {ScienceDirect Snapshot:/Users/yulei/Zotero/storage/AASUMP77/0951832096000026.html:text/html},
}

@article{kucherenko2019QuantileBasedGlobal,
	title = {Quantile based global sensitivity measures},
	volume = {185},
	issn = {0951-8320},
	url = {http://www.sciencedirect.com/science/article/pii/S0951832016304574},
	doi = {10.1016/j.ress.2018.12.001},
	abstract = {New global sensitivity measures based on quantiles of the output are introduced. Such measures can be used for global sensitivity analysis of problems in which αth quantiles are explicitly the functions of interest and for identification of variables which are the most important in achieving extreme values of the model output. It is proven that there is a link between introduced measures and Sobol’ main effect sensitivity indices. Two different Monte Carlo estimators are considered. It is shown that the double loop reordering approach is much more efficient than the brute force estimator. Several test cases and practical case studies related to structural safety are used to illustrate the developed method. Results of numerical calculations show the efficiency of the presented technique.},
	language = {en},
	urldate = {2020-07-17},
	journal = {Reliability Engineering \& System Safety},
	author = {Kucherenko, Sergei and Song, Shufang and Wang, Lu},
	month = may,
	year = {2019},
	keywords = {Global sensitivity analysis, Sobol’ sensitivity indices, Quantile based global sensitivity measure, Structural safety},
	pages = {35--48},
	file = {ScienceDirect Snapshot:/Users/yulei/Zotero/storage/VFLQI2N5/S0951832016304574.html:text/html;Kucherenko et al_2019_Quantile based global sensitivity measures.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Kucherenko et al_2019_Quantile based global sensitivity measures.pdf:application/pdf},
}

@article{eisenhauer2015EstimationDynamicDiscrete,
	title = {Estimation of {Dynamic} {Discrete} {Choice} {Models} by {Maximum} {Likelihood} and the {Simulated} {Method} of {Moments}},
	volume = {56},
	copyright = {© (2015) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association},
	issn = {1468-2354},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.1111/iere.12107},
	doi = {https://doi.org/10.1111/iere.12107},
	abstract = {We compare the performance of maximum likelihood (ML) and simulated method of moments (SMM) estimators for dynamic discrete choice models. We construct and estimate a simplified dynamic structural model of education that captures some basic features of educational choices in the United States in the 1980s and early 1990s. We use estimates from our model to simulate a synthetic data set and assess the ability of ML and SMM to recover the model parameters on this sample. We investigate the performance of alternative tuning parameters for SMM.},
	language = {en},
	number = {2},
	urldate = {2021-03-14},
	journal = {International Economic Review},
	author = {Eisenhauer, Philipp and Heckman, James J. and Mosso, Stefano},
	year = {2015},
	note = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1111/iere.12107},
	pages = {331--357},
	file = {Snapshot:/Users/yulei/Zotero/storage/ND2LCDZD/iere.html:text/html;Eisenhauer et al_2015_Estimation of Dynamic Discrete Choice Models by Maximum Likelihood and the.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Eisenhauer et al_2015_Estimation of Dynamic Discrete Choice Models by Maximum Likelihood and the.pdf:application/pdf},
}

@article{mcfadden1989MethodSimulatedMoments,
	title = {A {Method} of {Simulated} {Moments} for {Estimation} of {Discrete} {Response} {Models} {Without} {Numerical} {Integration}},
	volume = {57},
	issn = {00129682},
	url = {https://www.jstor.org/stable/1913621?origin=crossref},
	doi = {10.2307/1913621},
	abstract = {This paper proposes a simple modification of a conventional method of moments estimator for a discrete response model, replacing response probabilities that require numerical integration with estimators obtained by Monte Carlo simulation. This methodof simulated moments (MSM) does not require precise estimates of these probabilities for consistency and asymptotic normality, relying instead on the law of large numbers operating across observations to control simulation error, and hence can use simulations of practical size. The method is useful for models such as high-dimensional multinomial probit (MNP), where computation has restricted applications.},
	language = {en},
	number = {5},
	urldate = {2021-04-06},
	journal = {Econometrica},
	author = {McFadden, Daniel},
	month = sep,
	year = {1989},
	pages = {995},
	file = {McFadden_1989_A Method of Simulated Moments for Estimation of Discrete Response Models.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/McFadden_1989_A Method of Simulated Moments for Estimation of Discrete Response Models.pdf:application/pdf},
}

@article{kala2020QuantilebasedSobolSensitivity,
	title = {Quantile-based versus {Sobol} sensitivity analysis in limit state design},
	volume = {28},
	issn = {2352-0124},
	url = {https://www.sciencedirect.com/science/article/pii/S2352012420305993},
	doi = {10.1016/j.istruc.2020.10.037},
	abstract = {In limit state design, the reliability of building constructions is generally verified using design quantiles. The design resistance of a structure is explicitly expressed as a low quantile of the cumulative distribution function of resistance. The aim of this article is to show the connections and differences between quantile-oriented sensitivity analysis subordinated to a contrast and classic Sobol sensitivity analysis. Changing the fixed input variable causes synchronous change in the quantile and mean value, but how do the results of these two sensitivity analyses differ? The question is whether or not the changes around the design quantile (measured by contrast indices) are similar to the changes around the mean value, which are measured using Sobol’s indices. Comparison is performed on a case study, where the resistance of the structure is expressed by a non-linear function, the inputs of which are random material and geometric characteristics of the structure. The non-dimensional slenderness is a deterministic parameter, which changes the influence of input variables on the resistance as the model output. It was concluded upon comparing the results of both sensitivity analyses that the rank of the most important variables is the same for both low and high slenderness and is similar for intermediate slenderness. However, the interaction effects are very different. The identification of insignificant variables is the same. Other significant similarities and differences between both types of sensitivity analyses are presented in the article.},
	language = {en},
	urldate = {2021-04-07},
	journal = {Structures},
	author = {Kala, Zdeněk},
	month = dec,
	year = {2020},
	keywords = {Sensitivity analysis, Buckling, Design quantiles, Eurocodes, Stability, Steel, Structural reliability},
	pages = {2424--2430},
	file = {ScienceDirect Snapshot:/Users/yulei/Zotero/storage/JIRQ7HWG/S2352012420305993.html:text/html;Kala_2020_Quantile-based versus Sobol sensitivity analysis in limit state design.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Kala_2020_Quantile-based versus Sobol sensitivity analysis in limit state design.pdf:application/pdf},
}

@article{kala2021GlobalSensitivityAnalysis,
	title = {Global {Sensitivity} {Analysis} of {Quantiles}: {New} {Importance} {Measure} {Based} on {Superquantiles} and {Subquantiles}},
	volume = {13},
	copyright = {http://creativecommons.org/licenses/by/3.0/},
	shorttitle = {Global {Sensitivity} {Analysis} of {Quantiles}},
	url = {https://www.mdpi.com/2073-8994/13/2/263},
	doi = {10.3390/sym13020263},
	abstract = {The article introduces quantile deviation l as a new sensitivity measure based on the difference between superquantile and subquantile. New global sensitivity indices based on the square of l are presented. The proposed sensitivity indices are compared with quantile-oriented sensitivity indices subordinated to contrasts and classical Sobol sensitivity indices. The comparison is performed in a case study using a non-linear mathematical function, the output of which represents the elastic resistance of a slender steel member under compression. The steel member has random imperfections that reduce its load-carrying capacity. The member length is a deterministic parameter that significantly changes the sensitivity of the output resistance to the random effects of input imperfections. The comparison of the results of three types of global sensitivity analyses shows the rationality of the new quantile-oriented sensitivity indices, which have good properties similar to classical Sobol indices. Sensitivity indices subordinated to contrasts are the least comprehensible because they exhibit the strongest interaction effects between inputs. However, using total indices, all three types of sensitivity analyses lead to approximately the same conclusions. The similarity of the results of two quantile-oriented and Sobol sensitivity analysis confirms that Sobol sensitivity analysis is empathetic to the structural reliability and that the variance is one of the important characteristics significantly influencing the low quantile of resistance.},
	language = {en},
	number = {2},
	urldate = {2021-04-07},
	journal = {Symmetry},
	author = {Kala, Zdeněk},
	month = feb,
	year = {2021},
	note = {Number: 2
Publisher: Multidisciplinary Digital Publishing Institute},
	keywords = {quantile, sensitivity analysis, buckling, civil engineering, limit states, reliability, safety, subquantile, superquantile},
	pages = {263},
	file = {Snapshot:/Users/yulei/Zotero/storage/LI5HPQQ3/263.html:text/html;Kala_2021_Global Sensitivity Analysis of Quantiles.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Kala_2021_Global Sensitivity Analysis of Quantiles.pdf:application/pdf},
}

@article{eisenhauer2019ApproximateSolutionFinite,
	title = {The approximate solution of finite‐horizon discrete‐choice dynamic programming models},
	volume = {34},
	issn = {0883-7252, 1099-1255},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/jae.2648},
	doi = {10.1002/jae.2648},
	abstract = {The estimation of finite-horizon discrete-choice dynamic programming (DCDP) models is computationally expensive. This limits their realism and impedes verification and validation efforts. Keane and Wolpin (Review of Economics and Statistics, 1994, 76(4), 648–672) propose an interpolation method that ameliorates the computational burden but introduces approximation error. I describe their approach in detail, successfully recompute their original quality diagnostics, and provide some additional insights that underscore the trade-off between computation time and the accuracy of estimation results.},
	language = {en},
	number = {1},
	urldate = {2021-04-11},
	journal = {Journal of Applied Econometrics},
	author = {Eisenhauer, Philipp},
	month = jan,
	year = {2019},
	pages = {149--154},
	file = {Eisenhauer_2019_The approximate solution of finite‐horizon discrete‐choice dynamic programming.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Eisenhauer_2019_The approximate solution of finite‐horizon discrete‐choice dynamic programming.pdf:application/pdf},
}

@article{song2021QuantileSensitivityMeasures,
	title = {Quantile sensitivity measures based on subset simulation importance sampling},
	volume = {208},
	issn = {0951-8320},
	url = {https://www.sciencedirect.com/science/article/pii/S0951832020308917},
	doi = {10.1016/j.ress.2020.107405},
	abstract = {Global sensitivity measures based on quantiles of the output are an efficient tool in measuring the effect of input variables for problems in which α−th quantiles are the functions of interest and for identification of inputs which are the most important in achieving the specific values of the model output. Previously proposed methods for numerical estimation of such measures are costly and not practically feasible in cases in which the quantile level α is very small or high. It is shown that the subset simulation importance sampling (SS-IS) method previously applied for solving small failure probability problems can be efficiently used for estimating quantile global sensitivity measures (QGSM). Considered test cases and engineering examples show that the proposed SS-IS method is more efficient than the previously proposed Monte Carlo method.},
	language = {en},
	urldate = {2021-05-19},
	journal = {Reliability Engineering \& System Safety},
	author = {Song, Shufang and Bai, Zhiwei and Kucherenko, Sergei and Wang, Lu and Yang, Caiqiong},
	month = apr,
	year = {2021},
	keywords = {Importance sampling, Quantile sensitivity measures, Subset simulation, Variance-based global sensitivity indices},
	pages = {107405},
	file = {ScienceDirect Snapshot:/Users/yulei/Zotero/storage/D7LRAGAA/S0951832020308917.html:text/html;Song et al_2021_Quantile sensitivity measures based on subset simulation importance sampling.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Song et al_2021_Quantile sensitivity measures based on subset simulation importance sampling.pdf:application/pdf},
}

@article{song2009SubsetSimulationStructural,
	title = {Subset simulation for structural reliability sensitivity analysis},
	volume = {94},
	issn = {0951-8320},
	url = {https://www.sciencedirect.com/science/article/pii/S0951832008001944},
	doi = {10.1016/j.ress.2008.07.006},
	abstract = {Based on two procedures for efficiently generating conditional samples, i.e. Markov chain Monte Carlo (MCMC) simulation and importance sampling (IS), two reliability sensitivity (RS) algorithms are presented. On the basis of reliability analysis of Subset simulation (Subsim), the RS of the failure probability with respect to the distribution parameter of the basic variable is transformed as a set of RS of conditional failure probabilities with respect to the distribution parameter of the basic variable. By use of the conditional samples generated by MCMC simulation and IS, procedures are established to estimate the RS of the conditional failure probabilities. The formulae of the RS estimator, its variance and its coefficient of variation are derived in detail. The results of the illustrations show high efficiency and high precision of the presented algorithms, and it is suitable for highly nonlinear limit state equation and structural system with single and multiple failure modes.},
	language = {en},
	number = {2},
	urldate = {2021-05-20},
	journal = {Reliability Engineering \& System Safety},
	author = {Song, Shufang and Lu, Zhenzhou and Qiao, Hongwei},
	month = feb,
	year = {2009},
	keywords = {Conditional failure probability, Importance sampling (IS), Markov chain Monte Carlo (MCMC) simulation, Reliability sensitivity (RS), Subset simulation (Subsim)},
	pages = {658--665},
	file = {ScienceDirect Snapshot:/Users/yulei/Zotero/storage/MYAJVUSV/S0951832008001944.html:text/html;Song et al_2009_Subset simulation for structural reliability sensitivity analysis.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Song et al_2009_Subset simulation for structural reliability sensitivity analysis.pdf:application/pdf},
}

@report{eisenhauer2021StructuralModelsPolicymaking,
	title = {Structural models for policy-making: {Coping} with parametric uncertainty},
	shorttitle = {Structural models for policy-making},
	url = {https://arxiv.org/abs/2103.01115v2},
	abstract = {The ex-ante evaluation of policies using structural econometric models is based on estimated parameters as a stand-in for the truth. This practice ignores uncertainty in the counterfactual policy predictions of the model. We develop a generic approach that deals with parametric uncertainty using uncertainty sets and frames model-informed policymaking as a decision problem under uncertainty. The seminal human capital investment model by Keane and Wolpin (1997) provides us with a well-known, influential, and empirically-grounded test case. We document considerable uncertainty in their policy predictions and highlight the resulting policy recommendations from using different formal rules on decision-making under uncertainty.},
	language = {en},
	urldate = {2021-08-05},
	author = {Eisenhauer, Philipp and Gabler, Janoś and Janys, Lena},
	month = mar,
	year = {2021},
	keywords = {⛔ No DOI found},
	file = {Snapshot:/Users/yulei/Zotero/storage/VGBD3MHC/2103.html:text/html;Eisenhauer et al_2021_Structural models for policy-making.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Eisenhauer et al_2021_Structural models for policy-making.pdf:application/pdf},
}

@article{harenberg2019UncertaintyQuantificationGlobal,
	title = {Uncertainty quantification and global sensitivity analysis for economic models},
	volume = {10},
	issn = {1759-7331},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.3982/QE866},
	doi = {10.3982/QE866},
	abstract = {We present a global sensitivity analysis that quantifies the impact of parameter uncertainty on model outcomes. Specifically, we propose variance-decomposition-based Sobol' indices to establish an importance ranking of parameters and univariate effects to determine the direction of their impact. We employ the state-of-the-art approach of constructing a polynomial chaos expansion of the model, from which Sobol' indices and univariate effects are then obtained analytically, using only a limited number of model evaluations. We apply this analysis to several quantities of interest of a standard real-business-cycle model and compare it to traditional local sensitivity analysis approaches. The results show that local sensitivity analysis can be very misleading, whereas the proposed method accurately and efficiently ranks all parameters according to importance, identifying interactions and nonlinearities.},
	language = {en},
	number = {1},
	urldate = {2021-08-12},
	journal = {Quantitative Economics},
	author = {Harenberg, Daniel and Marelli, Stefano and Sudret, Bruno and Winschel, Viktor},
	year = {2019},
	note = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.3982/QE866},
	keywords = {sensitivity analysis, C60, C63, Computational techniques, polynomial chaos expansion, uncertainty quantification},
	pages = {1--41},
	file = {Snapshot:/Users/yulei/Zotero/storage/KRPWAPGC/QE866.html:text/html;Harenberg et al_2019_Uncertainty quantification and global sensitivity analysis for economic models.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Harenberg et al_2019_Uncertainty quantification and global sensitivity analysis for economic models.pdf:application/pdf},
}

@article{tennoe2018UncertainpyPythonToolbox,
	title = {Uncertainpy: {A} {Python} {Toolbox} for {Uncertainty} {Quantification} and {Sensitivity} {Analysis} in {Computational} {Neuroscience}},
	volume = {12},
	issn = {1662-5196},
	shorttitle = {Uncertainpy},
	url = {https://www.frontiersin.org/article/10.3389/fninf.2018.00049/full},
	doi = {10.3389/fninf.2018.00049},
	language = {en},
	urldate = {2021-08-18},
	journal = {Frontiers in Neuroinformatics},
	author = {Tennøe, Simen and Halnes, Geir and Einevoll, Gaute T.},
	month = aug,
	year = {2018},
	pages = {49},
	file = {Tennøe et al_2018_Uncertainpy.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Tennøe et al_2018_Uncertainpy.pdf:application/pdf},
}

@techreport{blesch2021RobustDecisionMakingRisk,
	title = {Robust {Decision}-{Making} {Under} {Risk} and {Ambiguity}},
	url = {https://ideas.repec.org/p/ajk/ajkdps/104.html},
	abstract = {Economists often estimate a subset of their model parameters outside the model and let the decision-makers inside the model treat these point estimates as-if they are correct. This practice ignores model ambiguity, opens the door for misspecification of the decision problem, and leads to post-decision disappointment. We develop a framework to explore, evaluate, and optimize decision rules that explicitly account for the uncertainty in the first step estimation using statistical decision theory. We show how to operationalize our analysis by studying a stochastic dynamic investment model where the decision-makers take ambiguity about the model's transition dynamics directly into account.},
	language = {en},
	number = {104},
	urldate = {2021-08-20},
	institution = {University of Bonn and University of Cologne, Germany},
	author = {Blesch, Maximilian and Eisenhauer, Philipp},
	month = jul,
	year = {2021},
	note = {Publication Title: ECONtribute Discussion Papers Series},
	keywords = {decision-making under uncertainty, robust Markov decision process},
	file = {Snapshot:/Users/yulei/Zotero/storage/V3BQCUSY/104.html:text/html;Blesch_Eisenhauer_2021_Robust Decision-Making Under Risk and Ambiguity.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Blesch_Eisenhauer_2021_Robust Decision-Making Under Risk and Ambiguity.pdf:application/pdf},
}

@article{lopiano2019NutritionPublicHealth,
	title = {Nutrition and public health economic evaluations under the lenses of post normal science},
	volume = {112},
	issn = {0016-3287},
	url = {https://www.sciencedirect.com/science/article/pii/S0016328718304087},
	doi = {10.1016/j.futures.2019.06.008},
	abstract = {The emerging scientific field of public health economics, considering health-related behaviours such as physical activity and smoking, is establishing itself as an important component in assessing the impact of policy interventions on preventing disease. Epidemiological evidence points to links between diet, lifestyle and non-communicable diseases (NCDs). Policy decisions aimed at preventing or reducing the burden of NCDs need credible, reliable and evidence-based scientific information. In this context, facts are uncertain and values are contested, while decisions are often urgent and the stakes are high, a typical setting for post-normal science (PNS). Therefore, this work applies quality tools developed in the context of PNS to models used in nutrition and public health economics, using as a guide the seven-point checklist of sensitivity auditing. This analysis has identified scope for improvement in a number of areas, such as the definition of the modelling exercise scope, the justification of the choice of family of models adopted, comprehensively framing the issue by including the perspective of relevant stakeholders and the exertion of more care in justifying assumptions. Addressing these dimensions may even result in refraining from producing a quantitative assessment when the circumstances do not hold. This would conflict with the common imperative to quantify in regulatory policies - often requested by policy guidelines - and with the dynamics of the policy cycle. For this reason, we discuss the implied trade-offs, contradictions and way forward with an eye to achieving progress in the practice.},
	language = {en},
	urldate = {2021-08-24},
	journal = {Futures},
	author = {Lo Piano, Samuele and Robinson, Marguerite},
	month = sep,
	year = {2019},
	keywords = {Sensitivity analysis, Cost-benefit analysis, Ethics of quantification, Health economics, Post-normal science, Sensitivity auditing},
	pages = {102436},
	file = {ScienceDirect Snapshot:/Users/yulei/Zotero/storage/YTT89VAF/S0016328718304087.html:text/html;Lo Piano_Robinson_2019_Nutrition and public health economic evaluations under the lenses of post.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Lo Piano_Robinson_2019_Nutrition and public health economic evaluations under the lenses of post.pdf:application/pdf},
}

@article{saltelli2015ClimateModelsEconomic,
	title = {Climate {Models} as {Economic} {Guides} {Scientific} {Challenge} or {Quixotic} {Quest}?},
	volume = {31},
	issn = {0748-5492},
	url = {https://www.jstor.org/stable/43314858},
	number = {3},
	urldate = {2021-08-24},
	journal = {Issues in Science and Technology},
	author = {SALTELLI, ANDREA and STARK, PHILIP B. and BECKER, WILLIAM and STANO, PAWEL},
	year = {2015},
	note = {Publisher: University of Texas at Dallas},
	keywords = {⛔ No DOI found},
	pages = {79--84},
	file = {SALTELLI et al_2015_Climate Models as Economic Guides Scientific Challenge or Quixotic Quest.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/SALTELLI et al_2015_Climate Models as Economic Guides Scientific Challenge or Quixotic Quest.pdf:application/pdf},
}

@misc{JRCPublicationsRepository,
	title = {{JRC} {Publications} {Repository} - {Climate} {Models} as {Economic} {Guides}: {Scientific} {Challenge} or {Quixotic} {Quest}?},
	url = {https://publications.jrc.ec.europa.eu/repository/handle/JRC94904},
	urldate = {2021-08-26},
	file = {JRC Publications Repository - Climate Models as Economic Guides\: Scientific Challenge or Quixotic Quest?:/Users/yulei/Zotero/storage/TCIDEYHG/JRC94904.html:text/html},
}

@article{saltelli2019WhyManyPublished,
	title = {Why so many published sensitivity analyses are false: {A} systematic review of sensitivity analysis practices},
	volume = {114},
	issn = {1364-8152},
	shorttitle = {Why so many published sensitivity analyses are false},
	url = {https://www.sciencedirect.com/science/article/pii/S1364815218302822},
	doi = {10.1016/j.envsoft.2019.01.012},
	abstract = {Sensitivity analysis provides information on the relative importance of model input parameters and assumptions. It is distinct from uncertainty analysis, which addresses the question ‘How uncertain is the prediction?’ Uncertainty analysis needs to map what a model does when selected input assumptions and parameters are left free to vary over their range of existence, and this is equally true of a sensitivity analysis. Despite this, many uncertainty and sensitivity analyses still explore the input space moving along one-dimensional corridors leaving space of the input factors mostly unexplored. Our extensive systematic literature review shows that many highly cited papers (42\% in the present analysis) fail the elementary requirement to properly explore the space of the input factors. The results, while discipline-dependent, point to a worrying lack of standards and recognized good practices. We end by exploring possible reasons for this problem, and suggest some guidelines for proper use of the methods.},
	language = {en},
	urldate = {2021-09-01},
	journal = {Environmental Modelling \& Software},
	author = {Saltelli, Andrea and Aleksankina, Ksenia and Becker, William and Fennell, Pamela and Ferretti, Federico and Holst, Niels and Li, Sushan and Wu, Qiongli},
	month = apr,
	year = {2019},
	pages = {29--39},
	file = {ScienceDirect Snapshot:/Users/yulei/Zotero/storage/U75ISW8F/S1364815218302822.html:text/html;Saltelli et al_2019_Why so many published sensitivity analyses are false.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Saltelli et al_2019_Why so many published sensitivity analyses are false.pdf:application/pdf},
}

@book{ghanem2017HandbookUncertaintyQuantification,
	address = {Cham},
	title = {Handbook of {Uncertainty} {Quantification}},
	isbn = {978-3-319-12384-4 978-3-319-12385-1},
	url = {http://link.springer.com/10.1007/978-3-319-12385-1},
	language = {en},
	urldate = {2021-09-01},
	publisher = {Springer International Publishing},
	editor = {Ghanem, Roger and Higdon, David and Owhadi, Houman},
	year = {2017},
	doi = {10.1007/978-3-319-12385-1},
	file = {Ghanem et al_2017_Handbook of Uncertainty Quantification.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Ghanem et al_2017_Handbook of Uncertainty Quantification.pdf:application/pdf},
}

@article{sobol2001GlobalSensitivityIndices,
	series = {The {Second} {IMACS} {Seminar} on {Monte} {Carlo} {Methods}},
	title = {Global sensitivity indices for nonlinear mathematical models and their {Monte} {Carlo} estimates},
	volume = {55},
	issn = {0378-4754},
	url = {https://www.sciencedirect.com/science/article/pii/S0378475400002706},
	doi = {10.1016/S0378-4754(00)00270-6},
	abstract = {Global sensitivity indices for rather complex mathematical models can be efficiently computed by Monte Carlo (or quasi-Monte Carlo) methods. These indices are used for estimating the influence of individual variables or groups of variables on the model output.},
	language = {en},
	number = {1},
	urldate = {2021-09-05},
	journal = {Mathematics and Computers in Simulation},
	author = {Sobol′, I. M},
	month = feb,
	year = {2001},
	keywords = {Sensitivity analysis, Mathematical modelling, Monte Carlo method, Quasi-Monte Carlo method},
	pages = {271--280},
	file = {ScienceDirect Snapshot:/Users/yulei/Zotero/storage/JGQHDIZL/S0378475400002706.html:text/html;Sobol′_2001_Global sensitivity indices for nonlinear mathematical models and their Monte.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Sobol′_2001_Global sensitivity indices for nonlinear mathematical models and their Monte.pdf:application/pdf},
}

@article{fort2016NewSensitivityAnalysis,
	title = {New sensitivity analysis subordinated to a contrast},
	volume = {45},
	issn = {0361-0926},
	url = {https://doi.org/10.1080/03610926.2014.901369},
	doi = {10.1080/03610926.2014.901369},
	abstract = {In a model of the form Y = h(X1, …, Xd) where the goal is to estimate a parameter of the probability distribution of Y, we define new sensitivity indices which quantify the importance of each variable Xi with respect to this parameter of interest. The aim of this paper is to define goal oriented sensitivity indices and we will show that Sobol indices are sensitivity indices associated to a particular characteristic of the distribution Y. We name the framework we present as Goal Oriented Sensitivity Analysis (GOSA).},
	number = {15},
	urldate = {2021-09-05},
	journal = {Communications in Statistics - Theory and Methods},
	author = {Fort, Jean-Claude and Klein, Thierry and Rachdi, Nabil},
	month = aug,
	year = {2016},
	note = {Publisher: Taylor \& Francis
\_eprint: https://doi.org/10.1080/03610926.2014.901369},
	keywords = {Sensitivity analysis, 62K99, 62P30, 65C60, 97M50, Sobol indices},
	pages = {4349--4364},
	file = {Snapshot:/Users/yulei/Zotero/storage/5UIZ9R4H/03610926.2014.html:text/html;Fort et al_2016_New sensitivity analysis subordinated to a contrast.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Fort et al_2016_New sensitivity analysis subordinated to a contrast.pdf:application/pdf},
}

@unpublished{browne2017EstimateQuantileorientedSensitivity,
	title = {Estimate of quantile-oriented sensitivity indices},
	url = {https://hal.archives-ouvertes.fr/hal-01450891},
	abstract = {In the context of black-box numerical codes, it is relevant to use sensitivity analysis in order to assess the influence of each random input X over the output Y. Goal-oriented sensitivity analysis states that one must first focus on a certain probability feature θ(Y) from the distribution of Y (such as its mean, quantile, or a probability of failure etc...), which would be chosen regarding a relevant strategy. The wish is to evaluate the impact of each input over θ(Y). In order to get supplementary information about sensitivity, we set that θ(Y) is the α-level quantile of Y , where α ∈]0, 1[. Throughout some examples, it has been pointed out that in some cases quantile-oriented sensitivity indices can detect some influence that Sobol indices would not. Mainly, the influence over each level of quantile displays how an input distribution entirely propagates through the output. We establish further results for the quantile-oriented indices properties in order to justify their relevancy. The main contribution of this paper comes when a statistical estimator for this index is introduced.},
	urldate = {2021-09-05},
	author = {Browne, Thomas and Fort, Jean-Claude and Iooss, Bertrand and Le Gratiet, Loïc},
	month = jan,
	year = {2017},
	keywords = {Sensitivity analysis, Sobol indices, goal-oriented sensitivity analysis, kernel-based estimators, output quantiles},
	file = {Browne et al_2017_Estimate of quantile-oriented sensitivity indices.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Browne et al_2017_Estimate of quantile-oriented sensitivity indices.pdf:application/pdf},
}

@article{maume-deschamps2018EstimationQuantileOriented,
	title = {Estimation of quantile oriented sensitivity indices},
	volume = {134},
	issn = {0167-7152},
	url = {https://www.sciencedirect.com/science/article/pii/S0167715217303413},
	doi = {10.1016/j.spl.2017.10.019},
	abstract = {This paper concerns quantile oriented sensitivity analysis (qosa). We rewrite the corresponding indices using the Conditional Tail Expectation risk measure. Then, we use this new expression to built estimators of qosa indices.},
	language = {en},
	urldate = {2021-09-05},
	journal = {Statistics \& Probability Letters},
	author = {Maume-Deschamps, Véronique and Niang, Ibrahima},
	month = mar,
	year = {2018},
	keywords = {Sensitivity analysis, Quantile oriented indices, Risk measures},
	pages = {122--127},
	file = {ScienceDirect Snapshot:/Users/yulei/Zotero/storage/F9NUSMYK/S0167715217303413.html:text/html;Maume-Deschamps_Niang_2018_Estimation of quantile oriented sensitivity indices.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Maume-Deschamps_Niang_2018_Estimation of quantile oriented sensitivity indices.pdf:application/pdf},
}

@article{cui2010MomentindependentImportanceMeasure,
	title = {Moment-independent importance measure of basic random variable and its probability density evolution solution},
	volume = {53},
	issn = {1862-281X},
	url = {https://doi.org/10.1007/s11431-009-0386-8},
	doi = {10.1007/s11431-009-0386-8},
	abstract = {To analyze the effect of basic variable on failure probability in reliability analysis, a moment-independent importance measure of the basic random variable is proposed, and its properties are analyzed and verified. Based on this work, the importance measure of the basic variable on the failure probability is compared with that on the distribution density of the response. By use of the probability density evolution method, a solution is established to solve two importance measures, which can efficiently avoid the difficulty in solving the importance measures. Some numerical examples and engineering examples are used to demonstrate the proposed importance measure on the failure probability and that on the distribution density of the response. The results show that the proposed importance measure can effectively describe the effect of the basic variable on the failure probability from the distribution density of the basic variable. Additionally, the results show that the established solution on the probability density evolution is efficient for the importance measures.},
	language = {en},
	number = {4},
	urldate = {2021-09-05},
	journal = {Science China Technological Sciences},
	author = {Cui, LiJie and Lü, ZhenZhou and Zhao, XinPan},
	month = apr,
	year = {2010},
	pages = {1138--1145},
	file = {Cui et al_2010_Moment-independent importance measure of basic random variable and its.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Cui et al_2010_Moment-independent importance measure of basic random variable and its.pdf:application/pdf},
}

@article{kucherenko2009MonteCarloEvaluation,
	series = {Special {Issue} on {Sensitivity} {Analysis}},
	title = {Monte {Carlo} evaluation of derivative-based global sensitivity measures},
	volume = {94},
	issn = {0951-8320},
	url = {https://www.sciencedirect.com/science/article/pii/S095183200800152X},
	doi = {10.1016/j.ress.2008.05.006},
	abstract = {A novel approach for evaluation of derivative-based global sensitivity measures (DGSM) is presented. It is compared with the Morris and the Sobol’ sensitivity indices methods. It is shown that there is a link between DGSM and Sobol’ sensitivity indices. DGSM are very easy to implement and evaluate numerically. The computational time required for numerical evaluation of DGSM is many orders of magnitude lower than that for estimation of the Sobol’ sensitivity indices. It is also lower than that for the Morris method. Efficiencies of Monte Carlo (MC) and quasi-Monte Carlo (QMC) sampling methods for calculation of DGSM are compared. It is shown that the superiority of QMC over MC depends on the problem's effective dimension, which can also be estimated using DGSM.},
	language = {en},
	number = {7},
	urldate = {2021-09-06},
	journal = {Reliability Engineering \& System Safety},
	author = {Kucherenko, S. and Rodriguez-Fernandez, M. and Pantelides, C. and Shah, N.},
	month = jul,
	year = {2009},
	keywords = {Global sensitivity analysis, Sobol’ sensitivity indices, Derivative-based global measures, Monte Carlo methods, Morris method, Quasi-Monte Carlo methods, Sobol’ sequences},
	pages = {1135--1148},
	file = {ScienceDirect Snapshot:/Users/yulei/Zotero/storage/AVT8CZG5/S095183200800152X.html:text/html;Kucherenko et al_2009_Monte Carlo evaluation of derivative-based global sensitivity measures.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Kucherenko et al_2009_Monte Carlo evaluation of derivative-based global sensitivity measures.pdf:application/pdf},
}

@article{sobol2009DerivativeBasedGlobal,
	title = {Derivative based global sensitivity measures and their link with global sensitivity indices},
	volume = {79},
	issn = {0378-4754},
	url = {https://www.sciencedirect.com/science/article/pii/S0378475409000354},
	doi = {10.1016/j.matcom.2009.01.023},
	abstract = {A model function f(x1,…,xn) defined in the unit hypercube Hn with Lebesque measure dx=dx1…dxn is considered. If the function is square integrable, global sensitivity indices provide adequate estimates for the influence of individual factors xi or groups of such factors. Alternative estimators that require less computer time can also be used. If the function f is differentiable, functionals depending on ∂f/∂xi have been suggested as estimators for the influence of xi. The Morris importance measure modified by Campolongo, Cariboni and Saltelli μ* is an approximation of the functional μi=∫Hn∂f/∂xidx. In this paper a similar functional is studiedνi=∫Hn∂f∂xi2dxEvidently, μi≤νi, and νi≤Cμi if ∂f/∂xi≤C. A link between νi and the sensitivity index Sitot is established:Sitot≤νiπ2Dwhere D is the total variance of f(x1,…,xn). Thus small νi imply small Sitot, and unessential factors xi (that is xi corresponding to a very small Sitot) can be detected analyzing computed values ν1,…,νn. However, ranking influential factors xi using these values can give false conclusions. Generalized Sitot and νi can be applied in situations where the factors x1,…,xn are independent random variables. If xi is a normal random variable with variance σi2, then Sitot≤νiσi2/D.},
	language = {en},
	number = {10},
	urldate = {2021-09-06},
	journal = {Mathematics and Computers in Simulation},
	author = {Sobol’, I. M. and Kucherenko, S.},
	month = jun,
	year = {2009},
	keywords = {Morris method, Derivative based global sensitivity measure, Global sensitivity index, Quasi Monte Carlo method},
	pages = {3009--3017},
	file = {ScienceDirect Snapshot:/Users/yulei/Zotero/storage/NHEFQPAN/S0378475409000354.html:text/html;Sobol’_Kucherenko_2009_Derivative based global sensitivity measures and their link with global.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Sobol’_Kucherenko_2009_Derivative based global sensitivity measures and their link with global.pdf:application/pdf},
}

@techreport{glynn1996ImportanceSamplingMonte,
	title = {Importance {Sampling} {For} {Monte} {Carlo} {Estimation} {Of} {Quantiles}},
	abstract = {This paper is concerned with applying importance sampling as a variance reduction tool for computing extreme quantiles. A central limit theorem is derived for each of four proposed importance sampling quantile estimators. Efficiency comparisons are provided in a certain asymptotic setting, using ideas from large deviation theory.  Keywords: quantiles, importance sampling, large deviations. 1 Introduction  Let X be a real-valued random variable with distribution function F ({\textbackslash}Delta). For 0 ! p ! 1, the quantity  F  {\textbackslash}Gamma1  (p)  4  = inffx : F (x)  pg  is called the p'th quantile of X. The quantile estimation problem is concerned with computing such quantities efficiently. Quantile estimation is of interest in many applications settings. For example, in computing tables of critical values associated with complicated hypothesis tests in which F cannot be computed analytically in closed form, it may be necessary to resort to Monte Carlo methodology as a means of calculating such critical v...},
	institution = {Publishing House of Saint Petersburg University},
	author = {Glynn, Peter W.},
	year = {1996},
	file = {Citeseer - Snapshot:/Users/yulei/Zotero/storage/SEJUVV2U/summary.html:text/html;Glynn_1996_Importance Sampling For Monte Carlo Estimation Of Quantiles.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Glynn_1996_Importance Sampling For Monte Carlo Estimation Of Quantiles.pdf:application/pdf},
}

@article{egloff2010QuantileEstimationAdaptive,
	title = {Quantile estimation with adaptive importance sampling},
	volume = {38},
	issn = {0090-5364, 2168-8966},
	url = {https://projecteuclid.org/journals/annals-of-statistics/volume-38/issue-2/Quantile-estimation-with-adaptive-importance-sampling/10.1214/09-AOS745.full},
	doi = {10.1214/09-AOS745},
	abstract = {We introduce new quantile estimators with adaptive importance sampling. The adaptive estimators are based on weighted samples that are neither independent nor identically distributed. Using a new law of iterated logarithm for martingales, we prove the convergence of the adaptive quantile estimators for general distributions with nonunique quantiles thereby extending the work of Feldman and Tucker [Ann. Math. Statist. 37 (1996) 451–457]. We illustrate the algorithm with an example from credit portfolio risk analysis.},
	number = {2},
	urldate = {2021-09-06},
	journal = {The Annals of Statistics},
	author = {Egloff, Daniel and Leippold, Markus},
	month = apr,
	year = {2010},
	note = {Publisher: Institute of Mathematical Statistics},
	keywords = {65C60, 62L20, 65C05, Adaptive importance sampling, Law of iterated logarithm, Quantile estimation, Robbins–Monro, stochastic approximation},
	pages = {1244--1278},
	file = {Snapshot:/Users/yulei/Zotero/storage/Q5BU2V85/09-AOS745.html:text/html;Egloff_Leippold_2010_Quantile estimation with adaptive importance sampling.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Egloff_Leippold_2010_Quantile estimation with adaptive importance sampling.pdf:application/pdf},
}

@article{oakley2004EstimatingPercentilesUncertain,
	title = {Estimating percentiles of uncertain computer code outputs},
	volume = {53},
	issn = {1467-9876},
	url = {https://rss.onlinelibrary.wiley.com/doi/abs/10.1046/j.0035-9254.2003.05044.x},
	doi = {10.1046/j.0035-9254.2003.05044.x},
	abstract = {Summary. A deterministic computer model is to be used in a situation where there is uncertainty about the values of some or all of the input parameters. This uncertainty induces uncertainty in the output of the model. We consider the problem of estimating a specific percentile of the distribution of this uncertain output. We also suppose that the computer code is computationally expensive, so we can run the model only at a small number of distinct inputs. This means that we must consider our uncertainty about the computer code itself at all untested inputs. We model the output, as a function of its inputs, as a Gaussian process, and after a few initial runs of the code use a simulation approach to choose further suitable design points and to make inferences about the percentile of interest itself. An example is given involving a model that is used in sewer design.},
	language = {en},
	number = {1},
	urldate = {2021-09-06},
	journal = {Journal of the Royal Statistical Society: Series C (Applied Statistics)},
	author = {Oakley, Jeremy},
	year = {2004},
	note = {\_eprint: https://rss.onlinelibrary.wiley.com/doi/pdf/10.1046/j.0035-9254.2003.05044.x},
	keywords = {Deterministic computer code, Gaussian process, Uncertainty distribution},
	pages = {83--93},
	file = {Snapshot:/Users/yulei/Zotero/storage/XWINWG5A/j.0035-9254.2003.05044.html:text/html;Oakley_2004_Estimating percentiles of uncertain computer code outputs.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Oakley_2004_Estimating percentiles of uncertain computer code outputs.pdf:application/pdf},
}

@article{saltelli2002SensitivityAnalysisImportance,
	title = {Sensitivity {Analysis} for {Importance} {Assessment}},
	volume = {22},
	issn = {1539-6924},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.1111/0272-4332.00040},
	doi = {10.1111/0272-4332.00040},
	abstract = {We review briefly some examples that would support an extended role for quantitative sensitivity analysis in the context of model-based analysis (Section 1). We then review what features a quantitative sensitivity analysis needs to have to play such a role (Section 2). The methods that meet these requirements are described in Section 3; an example is provided in Section 4. Some pointers to further research are set out in Section 5.},
	language = {en},
	number = {3},
	urldate = {2021-09-06},
	journal = {Risk Analysis},
	author = {Saltelli, Andrea},
	year = {2002},
	note = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1111/0272-4332.00040},
	keywords = {risk analysis, Uncertainty analysis, assessment of importance, computational models, quantitative sensitivity analysis},
	pages = {579--590},
	file = {Snapshot:/Users/yulei/Zotero/storage/K3T6C87F/0272-4332.html:text/html;Saltelli_2002_Sensitivity Analysis for Importance Assessment.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Saltelli_2002_Sensitivity Analysis for Importance Assessment.pdf:application/pdf},
}

@article{marino2008MethodologyPerformingGlobal,
	title = {A {Methodology} {For} {Performing} {Global} {Uncertainty} {And} {Sensitivity} {Analysis} {In} {Systems} {Biology}},
	volume = {254},
	issn = {0022-5193},
	url = {https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2570191/},
	doi = {10.1016/j.jtbi.2008.04.011},
	abstract = {Accuracy of results from mathematical and computer models of biological systems is often complicated by the presence of uncertainties in experimental data that are used to estimate parameter values. Current mathematical modeling approaches typically use either single-parameter or local sensitivity analyses. However, these methods do not accurately assess uncertainty and sensitivity in the system as, by default they hold all other parameters fixed at baseline values. Using techniques described within we demonstrate how a multi-dimensional parameter space can be studied globally so all uncertainties can be identified. Further, uncertainty and sensitivity analysis techniques can help to identify and ultimately control uncertainties. In this work we develop methods for applying existing analytical tools to perform analyses on a variety of mathematical and computer models. We compare two specific types of global sensitivity analysis indexes that have proven to be among the most robust and efficient. Through familiar and new examples of mathematical and computer models, we provide a complete methodology for performing these analyses, both in deterministic and stochastic settings, and propose novel techniques to handle problems encountered during this type of analyses.},
	number = {1},
	urldate = {2021-09-06},
	journal = {Journal of theoretical biology},
	author = {Marino, Simeone and Hogue, Ian B. and Ray, Christian J. and Kirschner, Denise E.},
	month = sep,
	year = {2008},
	pmid = {18572196},
	pmcid = {PMC2570191},
	pages = {178--196},
	file = {Marino et al_2008_A Methodology For Performing Global Uncertainty And Sensitivity Analysis In.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Marino et al_2008_A Methodology For Performing Global Uncertainty And Sensitivity Analysis In.pdf:application/pdf},
}

@article{zi2011SensitivityAnalysisApproaches,
	title = {Sensitivity analysis approaches applied to systems biology models},
	volume = {5},
	issn = {1751-8849},
	doi = {10.1049/iet-syb.2011.0015},
	abstract = {With the rising application of systems biology, sensitivity analysis methods have been widely applied to study the biological systems, including metabolic networks, signalling pathways and genetic circuits. Sensitivity analysis can provide valuable insights about how robust the biological responses are with respect to the changes of biological parameters and which model inputs are the key factors that affect the model outputs. In addition, sensitivity analysis is valuable for guiding experimental analysis, model reduction and parameter estimation. Local and global sensitivity analysis approaches are the two types of sensitivity analysis that are commonly applied in systems biology. Local sensitivity analysis is a classic method that studies the impact of small perturbations on the model outputs. On the other hand, global sensitivity analysis approaches have been applied to understand how the model outputs are affected by large variations of the model input parameters. In this review, the author introduces the basic concepts of sensitivity analysis approaches applied to systems biology models. Moreover, the author discusses the advantages and disadvantages of different sensitivity analysis methods, how to choose a proper sensitivity analysis approach, the available sensitivity analysis tools for systems biology models and the caveats in the interpretation of sensitivity analysis results.},
	language = {eng},
	number = {6},
	journal = {IET systems biology},
	author = {Zi, Z.},
	month = nov,
	year = {2011},
	pmid = {22129029},
	keywords = {Software, Models, Biological, Systems Biology},
	pages = {336--336},
	file = {Zi_2011_Sensitivity analysis approaches applied to systems biology models.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Zi_2011_Sensitivity analysis approaches applied to systems biology models.pdf:application/pdf},
}

@article{pannell1997SensitivityAnalysisNormative,
	title = {Sensitivity analysis of normative economic models: theoretical framework and practical strategies},
	volume = {16},
	issn = {0169-5150},
	shorttitle = {Sensitivity analysis of normative economic models},
	url = {https://www.sciencedirect.com/science/article/pii/S0169515096012170},
	doi = {10.1016/S0169-5150(96)01217-0},
	abstract = {The parameter values and assumptions of any economic model are subject to change and error. Sensitivity analysis (SA), broadly defined, is the investigation of these potential changes and errors and their impacts on conclusions to be drawn from the model. There is a very large literature on procedures and techniques for SA, but it includes almost nothing from economists. This paper is a selective review and overview of theoretical and methodological issues in SA. There are many possible uses of SA, described here within the categories of decision support, communication, increased understanding or quantification of the system, and model development. The paper focuses somewhat on decision support. It is argued that even the simplest approaches to SA can be theoretically respectable in decision support if they are applied and interpreted in a way consistent with Bayesian decision theory. This is not to say that SA results should be formally subjected to a Bayesian decision analysis, but that an understanding of Bayesian probability revision will help the modeller plan and interpret an SA. Many different approaches to SA are described, varying in the experimental design used and in the way results are processed. Possible overall strategies for conducting SA are suggested. It is proposed that when using SA for decision support, it can be very helpful to attempt to identify which of the following forms of recommendation is most appropriate: (a) do X, (b) do either X or Y depending on the circumstances, (c) do either X or Y, whichever you like, (d) if in doubt, do X. A system for reporting and discussing SA results is recommended.},
	language = {en},
	number = {2},
	urldate = {2021-09-06},
	journal = {Agricultural Economics},
	author = {Pannell, David J.},
	month = may,
	year = {1997},
	pages = {139--152},
	file = {Pannell_1997_Sensitivity analysis of normative economic models.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Pannell_1997_Sensitivity analysis of normative economic models.pdf:application/pdf},
}

@article{degenring2004SensitivityAnalysisReduction,
	series = {Dynamics, {Monitoring}, {Control} and {Optimization} of {Biological} {Systems}},
	title = {Sensitivity analysis for the reduction of complex metabolism models},
	volume = {14},
	issn = {0959-1524},
	url = {https://www.sciencedirect.com/science/article/pii/S0959152403001379},
	doi = {10.1016/j.jprocont.2003.12.008},
	abstract = {Two different model reduction strategies are studied in order to test their applicability to reduce complex metabolism models. Using a model of one pre-identified model set describing complex metabolic dynamics after glucose pulse stimulation, a model reduction method based on the parameter tuning importance is compared with a pca based approach. Up to 49 of 122 parameters are rejected without significant changes of the simulated trajectories and of the flux distribution. Applying the reduction procedure to 12 other dynamic models reveals a general model structure inconsistency within the description of the pentose phosphate pathway. That points out the need of additional experiments to reproduce metabolite courses especially of this metabolic pathway. Thus the sensitivity based model reduction procedure is qualified as a promising tool for the model structure check and can be very useful for the entire model validation process which also includes the critical analysis of the data sets underlying the models.},
	language = {en},
	number = {7},
	urldate = {2021-09-06},
	journal = {Journal of Process Control},
	author = {Degenring, D. and Froemel, C. and Dikta, G. and Takors, R.},
	month = oct,
	year = {2004},
	keywords = {Metabolism, Model reduction, Model validation, Parameter sensitivity, Pca},
	pages = {729--745},
	file = {ScienceDirect Snapshot:/Users/yulei/Zotero/storage/8UX736BH/S0959152403001379.html:text/html;Degenring et al_2004_Sensitivity analysis for the reduction of complex metabolism models.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Degenring et al_2004_Sensitivity analysis for the reduction of complex metabolism models.pdf:application/pdf},
}

@article{feinberg2015ChaospyOpenSource,
	title = {Chaospy: {An} open source tool for designing methods of uncertainty quantification},
	volume = {11},
	issn = {1877-7503},
	shorttitle = {Chaospy},
	url = {https://www.sciencedirect.com/science/article/pii/S1877750315300119},
	doi = {10.1016/j.jocs.2015.08.008},
	abstract = {The paper describes the philosophy, design, functionality, and usage of the Python software toolbox Chaospy for performing uncertainty quantification via polynomial chaos expansions and Monte Carlo simulation. The paper compares Chaospy to similar packages and demonstrates a stronger focus on defining reusable software building blocks that can easily be assembled to construct new, tailored algorithms for uncertainty quantification. For example, a Chaospy user can in a few lines of high-level computer code define custom distributions, polynomials, integration rules, sampling schemes, and statistical metrics for uncertainty analysis. In addition, the software introduces some novel methodological advances, like a framework for computing Rosenblatt transformations and a new approach for creating polynomial chaos expansions with dependent stochastic variables.},
	language = {en},
	urldate = {2021-09-06},
	journal = {Journal of Computational Science},
	author = {Feinberg, Jonathan and Langtangen, Hans Petter},
	month = nov,
	year = {2015},
	keywords = {Monte Carlo simulation, Uncertainty quantification, Polynomial chaos expansions, Python package, Rosenblatt transformations},
	pages = {46--57},
	file = {ScienceDirect Snapshot:/Users/yulei/Zotero/storage/4UZJP8TC/S1877750315300119.html:text/html;Feinberg_Langtangen_2015_Chaospy.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Feinberg_Langtangen_2015_Chaospy.pdf:application/pdf},
}

@article{herman2017SALibOpensourcePython,
	title = {{SALib}: {An} open-source {Python} library for {Sensitivity} {Analysis}},
	volume = {2},
	issn = {2475-9066},
	shorttitle = {{SALib}},
	url = {https://joss.theoj.org/papers/10.21105/joss.00097},
	doi = {10.21105/joss.00097},
	abstract = {Herman et al, (2017), SALib: An open-source Python library for Sensitivity Analysis, Journal of Open Source Software, 2(9), 97, doi:10.21105/joss.00097},
	language = {en},
	number = {9},
	urldate = {2021-09-06},
	journal = {Journal of Open Source Software},
	author = {Herman, Jon and Usher, Will},
	month = jan,
	year = {2017},
	pages = {97},
	file = {Snapshot:/Users/yulei/Zotero/storage/6Z7CKAWX/joss.html:text/html;Herman_Usher_2017_SALib.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Herman_Usher_2017_SALib.pdf:application/pdf},
}

@book{wolpin2013LimitsInferenceTheory,
	address = {Cambridge, MA, USA},
	series = {Tjalling {C}. {Koopmans} {Memorial} {Lectures}},
	title = {The {Limits} of {Inference} without {Theory}},
	isbn = {978-0-262-01908-8},
	abstract = {The role of theory in ex ante policy evaluations and the limits that eschewing theory places on inference},
	language = {en},
	publisher = {MIT Press},
	author = {Wolpin, Kenneth I.},
	editor = {Samuelson, Larry},
	month = apr,
	year = {2013},
}

@article{saltelli2020FiveWaysEnsure,
	title = {Five ways to ensure that models serve society: a manifesto},
	volume = {582},
	copyright = {2021 Nature},
	shorttitle = {Five ways to ensure that models serve society},
	url = {https://www.nature.com/articles/d41586-020-01812-9},
	doi = {10.1038/d41586-020-01812-9},
	abstract = {Pandemic politics highlight how predictions need to be transparent and humble to invite insight, not blame.},
	language = {en},
	number = {7813},
	urldate = {2021-09-06},
	journal = {Nature},
	author = {Saltelli, Andrea and Bammer, Gabriele and Bruno, Isabelle and Charters, Erica and Di Fiore, Monica and Didier, Emmanuel and Nelson Espeland, Wendy and Kay, John and Lo Piano, Samuele and Mayo, Deborah and Pielke Jr, Roger and Portaluri, Tommaso and Porter, Theodore M. and Puy, Arnald and Rafols, Ismael and Ravetz, Jerome R. and Reinert, Erik and Sarewitz, Daniel and Stark, Philip B. and Stirling, Andrew and van der Sluijs, Jeroen and Vineis, Paolo},
	month = jun,
	year = {2020},
	note = {Bandiera\_abtest: a
Cg\_type: Comment
Number: 7813
Publisher: Nature Publishing Group
Subject\_term: Communication, Policy, Epidemiology},
	pages = {482--484},
	file = {Snapshot:/Users/yulei/Zotero/storage/QMZ8GA8Q/d41586-020-01812-9.html:text/html;Saltelli et al_2020_Five ways to ensure that models serve society.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Saltelli et al_2020_Five ways to ensure that models serve society.pdf:application/pdf},
}

@book{nationalresearchcouncil2012AssessingReliabilityComplex,
	address = {Washington, DC},
	title = {Assessing the {Reliability} of {Complex} {Models}: {Mathematical} and {Statistical} {Foundations} of {Verification}, {Validation}, and {Uncertainty} {Quantification}},
	isbn = {978-0-309-25634-6},
	shorttitle = {Assessing the {Reliability} of {Complex} {Models}},
	url = {https://www.nap.edu/catalog/13395/assessing-the-reliability-of-complex-models-mathematical-and-statistical-foundations},
	abstract = {Advances in computing hardware and algorithms have dramatically improved the ability to simulate complex processes computationally. Today's simulation capabilities offer the prospect of addressing questions that in the past could be addressed only by resource-intensive experimentation, if at all. Assessing the Reliability of Complex Models recognizes the ubiquity of uncertainty in computational estimates of reality and the necessity for its quantification.
As computational science and engineering have matured, the process of quantifying or bounding uncertainties in a computational estimate of a physical quality of interest has evolved into a small set of interdependent tasks: verification, validation, and uncertainty of quantification (VVUQ). In recognition of the increasing importance of computational simulation and the increasing need to assess uncertainties in computational results, the National Research Council was asked to study the mathematical foundations of VVUQ and to recommend steps that will ultimately lead to improved processes.
Assessing the Reliability of Complex Models discusses changes in education of professionals and dissemination of information that should enhance the ability of future VVUQ practitioners to improve and properly apply VVUQ methodologies to difficult problems, enhance the ability of VVUQ customers to understand VVUQ results and use them to make informed decisions, and enhance the ability of all VVUQ stakeholders to communicate with each other. This report is an essential resource for all decision and policy makers in the field, students, stakeholders, UQ experts, and VVUQ educators and practitioners.},
	language = {English},
	urldate = {2021-09-06},
	publisher = {The National Academies Press},
	author = {National Research Council},
	year = {2012},
	doi = {10.17226/13395},
	keywords = {Math, Chemistry, and Physics, Surveys and Statistics},
}

@book{scienceadviceforpolicybyeuropeanacademies2019MakingSenseScience,
	address = {DE},
	title = {Making sense of science for policy under conditions of complexity and uncertainty},
	url = {https://doi.org/10.26356/masos},
	language = {en},
	urldate = {2021-09-06},
	publisher = {Science Advice for Policy by European Academies},
	author = {{Science Advice for Policy by European Academies}},
	year = {2019},
	file = {Science Advice for Policy by European Academies_2019_Making sense of science for policy under conditions of complexity and.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Science Advice for Policy by European Academies_2019_Making sense of science for policy under conditions of complexity and.pdf:application/pdf},
}

@incollection{keane2011ChapterStructuralEstimation,
	title = {Chapter 4 - {The} {Structural} {Estimation} of {Behavioral} {Models}: {Discrete} {Choice} {Dynamic} {Programming} {Methods} and {Applications}},
	volume = {4},
	shorttitle = {Chapter 4 - {The} {Structural} {Estimation} of {Behavioral} {Models}},
	url = {https://www.sciencedirect.com/science/article/pii/S0169721811004102},
	abstract = {The purpose of this chapter is twofold: (1) to provide an accessible introduction to the methods of structural estimation of discrete choice dynamic programming (DCDP) models and (2) to survey the contributions of applications of these methods to substantive and policy issues in labor economics. The first part of the chapter describes solution and estimation methods for DCDP models using, for expository purposes, a prototypical female labor force participation model. The next part reviews the contribution of the DCDP approach to three leading areas in labor economics: labor supply, job search and human capital. The final section discusses approaches to validating DCDP models.},
	language = {en},
	urldate = {2021-09-06},
	booktitle = {Handbook of {Labor} {Economics}},
	publisher = {Elsevier},
	author = {Keane, Michael P. and Todd, Petra E. and Wolpin, Kenneth I.},
	editor = {Ashenfelter, Orley and Card, David},
	month = jan,
	year = {2011},
	doi = {10.1016/S0169-7218(11)00410-2},
	keywords = {Discrete choice, Dynamic programming, Human capital, Job search, Labor supply, Structural estimation},
	pages = {331--461},
	file = {ScienceDirect Snapshot:/Users/yulei/Zotero/storage/NV3GRPW5/S0169721811004102.html:text/html;Keane et al_2011_Chapter 4 - The Structural Estimation of Behavioral Models.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Keane et al_2011_Chapter 4 - The Structural Estimation of Behavioral Models.pdf:application/pdf},
}

@article{adda2017CareerCostsChildren,
	title = {The {Career} {Costs} of {Children}},
	volume = {125},
	issn = {0022-3808},
	url = {https://www.journals.uchicago.edu/doi/abs/10.1086/690952},
	doi = {10.1086/690952},
	abstract = {We estimate a dynamic life cycle model of labor supply, fertility, and savings, incorporating occupational choices, with specific wage paths and skill atrophy that vary over the career. This allows us to understand the trade-off between occupational choice and desired fertility, as well as sorting both into the labor market and across occupations. We quantify the life cycle career costs associated with children, how they decompose into loss of skills during interruptions, lost earnings opportunities, and selection into more child-friendly occupations. We analyze the long-run effects of policies that encourage fertility and show that they are considerably smaller than short-run effects.},
	number = {2},
	urldate = {2021-09-06},
	journal = {Journal of Political Economy},
	author = {Adda, Jérôme and Dustmann, Christian and Stevens, Katrien},
	month = apr,
	year = {2017},
	note = {Publisher: The University of Chicago Press},
	pages = {293--337},
	file = {Adda et al_2017_The Career Costs of Children.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Adda et al_2017_The Career Costs of Children.pdf:application/pdf},
}

@article{blundell2016FemaleLaborSupply,
	title = {Female {Labor} {Supply}, {Human} {Capital}, and {Welfare} {Reform}},
	volume = {84},
	issn = {1468-0262},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.3982/ECTA11576},
	doi = {10.3982/ECTA11576},
	abstract = {We estimate a dynamic model of employment, human capital accumulation—including education, and savings for women in the United Kingdom, exploiting tax and benefit reforms, and use it to analyze the effects of welfare policy. We find substantial elasticities for labor supply and particularly for lone mothers. Returns to experience, which are important in determining the longer-term effects of policy, increase with education, but experience mainly accumulates when in full-time employment. Tax credits are welfare improving in the U.K., increase lone-mother labor supply and marginally reduce educational attainment, but the employment effects do not extend beyond the period of eligibility. Marginal increases in tax credits improve welfare more than equally costly increases in income support or tax cuts.},
	language = {en},
	number = {5},
	urldate = {2021-09-06},
	journal = {Econometrica},
	author = {Blundell, Richard and Dias, Monica Costa and Meghir, Costas and Shaw, Jonathan},
	year = {2016},
	note = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.3982/ECTA11576},
	keywords = {education, female labor supply, human capital, income tax, learning by doing, Life-cycle model, negative income tax, part time work, subsidies},
	pages = {1705--1753},
	file = {Snapshot:/Users/yulei/Zotero/storage/2NIX2V7F/ECTA11576.html:text/html;Blundell et al_2016_Female Labor Supply, Human Capital, and Welfare Reform.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Blundell et al_2016_Female Labor Supply, Human Capital, and Welfare Reform.pdf:application/pdf},
}

@article{eckstein2019CareerFamilyDecisions,
	title = {Career and {Family} {Decisions}: {Cohorts} {Born} 1935-1975},
	volume = {87},
	issn = {0012-9682},
	shorttitle = {Career and {Family} {Decisions}},
	url = {https://www.econometricsociety.org/doi/10.3982/ECTA14474},
	doi = {10.3982/ECTA14474},
	language = {en},
	number = {1},
	urldate = {2021-09-06},
	journal = {Econometrica},
	author = {Eckstein, Zvi and Keane, Michael and Lifshitz, Osnat},
	year = {2019},
	pages = {217--253},
	file = {Eckstein et al_2019_Career and Family Decisions.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Eckstein et al_2019_Career and Family Decisions.pdf:application/pdf},
}

@article{manski2021EconometricsDecisionMaking,
	title = {Econometrics {For} {Decision} {Making}: {Building} {Foundations} {Sketched} {By} {Haavelmo} {And} {Wald}},
	shorttitle = {Econometrics {For} {Decision} {Making}},
	url = {http://arxiv.org/abs/1912.08726},
	abstract = {Haavelmo (1944) proposed a probabilistic structure for econometric modeling, aiming to make econometrics useful for decision making. His fundamental contribution has become thoroughly embedded in subsequent econometric research, yet it could not answer all the deep issues that the author raised. Notably, Haavelmo struggled to formalize the implications for decision making of the fact that models can at most approximate actuality. In the same period, Wald (1939, 1945) initiated his own seminal development of statistical decision theory. Haavelmo favorably cited Wald, but econometrics did not embrace statistical decision theory. Instead, it focused on study of identification, estimation, and statistical inference. This paper proposes statistical decision theory as a framework for evaluation of the performance of models in decision making. I particularly consider the common practice of as-if optimization: specification of a model, point estimation of its parameters, and use of the point estimate to make a decision that would be optimal if the estimate were accurate. A central theme is that one should evaluate as-if optimization or any other model-based decision rule by its performance across the state space, listing all states of nature that one believes feasible, not across the model space. I apply the theme to prediction and treatment choice. Statistical decision theory is conceptually simple, but application is often challenging. Advancement of computation is the primary task to continue building the foundations sketched by Haavelmo and Wald.},
	urldate = {2021-09-06},
	journal = {arXiv:1912.08726 [econ]},
	author = {Manski, Charles F.},
	month = feb,
	year = {2021},
	note = {arXiv: 1912.08726},
	keywords = {⛔ No DOI found, Economics - Econometrics},
	file = {arXiv.org Snapshot:/Users/yulei/Zotero/storage/YSMRK5JZ/1912.html:text/html;Manski_2021_Econometrics For Decision Making.pdf:/Users/yulei/Dropbox/ZoteroAttachments/master thesis/Manski_2021_Econometrics For Decision Making.pdf:application/pdf},
}

@techreport{janosgabler20