TITLE: Easier reference for material like Diaconis's "Group representations in probability and statistics"
QUESTION [20 upvotes]: I'm teaching a class on the representation theory of finite groups at the advanced undergrad level.  One of the things I'd like to talk about, or possibly have a student do any independent project on is applications of finite groups in statistics and data analysis.  Unfortunately, the only book I know on the subject is Persi Diaconis's Group representations in probability and statistics, which is lovely but nowhere close to the level that I would expect an undergrad to read (or for that matter, anyone from a field outside math).  Are there any books or articles people know of which provide a gentler introduction?

REPLY [7 votes]: This 74-page paper in Journal of Machine Learning Research (by Huang, Guestrin, and Guibas) --
http://www.jmlr.org/papers/volume10/huang09a/huang09a.pdf
-- is an amazingly useful and undergrad-friendly intro to the representation theory of the symmetric group (in a very surprising venue).  Also, the fact that its applications are to machine learning and statistics looks very appropriate for OP's question.

REPLY [3 votes]: The book Probability on Discrete Structures contains a chapter called "Random walks on finite groups" by Laurent Saloff-Coste which predates Benjamin Steinberg's book.