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lukeprog comments on Open Thread, October 27 - 31, 2013 - Less Wrong
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Could anyone provide me with some rigorous mathematical references on Statistical Hypotheses Testing, and Bayesian Decision Theory? I am not an expert in this area, and am not aware of the standard texts. So far I have found
Currently, I am leaning towards purchasing Berger's book. I am looking for texts similar in style and content to those of Springer's GTM series. It looks like the Springer Series in Statistics may be sufficient.
Berger is highly technical, not much of an introduction.
On Bayesian statistics, Bayesian Data Analaysis is a classic.
"Bayesian decision theory" usually just means "normal decision theory," so you could start with my FAQ. Though when decision theory is taught from a statistics book rather than an economic book, they use slightly different terminology, e.g. they set things up with a loss function rather than a utility function. For an intro to decision theory from the Bayesian statistics angle, Introduction to Statistical Decision Theory is pretty thorough, and more accessible than Berger.
Great, thank you very much for the references. I am now reading your FAQ before moving onto the texts, I'll post any comments I have there.