TITLE: Bayesian statistics for pure mathematicians
QUESTION [25 upvotes]: Could someone please recommend reading on Bayesian statistics presented from a pure mathematical point of view?  That is, works that start assuming a good knowledge of measure theoretic probability.  The usual reference works for statisticians gloss over the fine details, but for me this just leads to more confusion!
I already know of the following question
Statistics for mathematicians
and will follow up some of the suggestions there, but I am specifically looking for a treatment of the Bayesian approach, so if there are any recommendations that apply just to this I would appreciate hearing about them.

REPLY [3 votes]: There is a book of 2018 on the topic, that also presents some recent results of the author:

S. Watanabe, Mathematical Theory of Bayesian Statistics, Chapman and Hall/CRC, Apr 2018