There’s a short discussion in Bishop’s Pattern Recognition and Machine Learning, which is easier than Berger (and much shorter — it’s one introductory section). I also looked up the discussion of decision theory in MacKay’s info theory and machine learning book — there’s two pages of example after a discussion and a dismissal of the topic as “trivial” (though not unimportant, of course — it’s just that it follows pretty directly from everything else).

I don’t know Lindley’s book, but Lindley did some fundamental research in Bayesian stats. On the more philosophical side, he introduced what is now known as Lindley’s Paradox (Wikipedia).

It looks like Lindley also has a book for the general public called Understanding Uncertainty.

There are really two courses of study. There’s the whole philosophy of Bayesian statistics side, which is often motivated decision-theoretically. This is both about the philosophy of science and reasoning in general and about human reasoning and epistemology (this is where Kyburg is relevant).

Then there’s the actual apparatus to carry out model fitting given some notion of loss that you want to apply. Berger’s book covers both, but it’s basically a math book with some background philosophy. I assume Lindley would cover both the math and the philosophy — he was active on both sides.

• Berger, James O. 1985. Statistical Decision Theory and Bayesian Analysis. 2nd Edition. Springer.

Some of the fundamental motivations for Bayesian statistics are decision theoretic (in the sense that if you don’t follow the proper Bayesian inferences you can be taken advantage of in a betting context, i.e., they can make Dutch book against you (ed. whenever “Dutch” appears as an adjective in English, you know it’s something distasteful; c.f., “Dutch uncle”, “Dutch date”, “double Dutch”).

For a quick intro to what makes Bayesian stats Bayesian, along with an overview of the inferential apparatus, see my earlier post, What is Bayesian Statistical Inference?.

You can, of course, use decision theory in a frequentist setting or even in non-probabilistic settings with the right formulation.

Thanks!