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What is a good book about Bayesian philosophy, contrasting subjectivists against objectivists, explaining the view of probability as state of knowledge in Bayesian statistics, etc.? Maybe Savage's book?

At first I thought Berger (1986) could work, but it is not what I am looking for. Searching for such a book just doesn't quite lead to the results I am looking for.

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  • $\begingroup$ possible duplicate of What is the best introductory Bayesian statistics textbook? $\endgroup$ – Tim Feb 15 '15 at 15:44
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    $\begingroup$ Barnett's book systematically compares Bayesian and frequentist approaches: amazon.com/Comparative-Statistical-Inference-Vic-Barnett/dp/… $\endgroup$ – Zen Feb 15 '15 at 15:48
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    $\begingroup$ The linked thread seems to be mostly about introductions to doing Bayesian analyses, rather than the specific philosophies. This may be distinct enough to remain open. $\endgroup$ – gung Feb 15 '15 at 16:11
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    $\begingroup$ Can you be more specific? Why isn't Berger what you were looking for? What are the results you are looking for? How will you recognize when you've found the kind of book you are looking for? How will you evaluate answers? Asking for "a good book" is vague and subjective; can you edit your question to give us more precise requirements? $\endgroup$ – D.W. Feb 15 '15 at 21:14
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Jay Kadane's Principles of uncertainty is a recent and highly coherent introduction to subjective Bayesian thinking. I reviewed it there and definitely recommend it.

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    $\begingroup$ (+1) Great suggestion. Your own "Bayesian Choice" is another excellent option. $\endgroup$ – Zen Feb 15 '15 at 16:08
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    $\begingroup$ @Zen: Thanks! But I do not pretend at mastering the philosophy of subjectivism!!! $\endgroup$ – Xi'an Feb 15 '15 at 17:34
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    $\begingroup$ Anyway, Chapter 11 (A Defense of the Bayesian Choice) is very convincing. $\endgroup$ – Zen Feb 15 '15 at 17:37
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I'm a particular fan of Understanding Uncertainty by Dennis Lindley. I actually emailed Jay Kadane a while back to ask the same question you did, and he recommended me this book.

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Probability, The Logic of Science by E.T. Jaynes, provides excellent discussions around this subject. Jaynes is on the side of Objective Bayesianism.

Related books that influenced Jaynes' book are Jeffreys' Theory of Probability of 1939 (1948, 1961), Good's Probability & the Weighing of Evidence of 1950 and Savage's Foundations of Statistics of 1954.

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Here is a recent title with a focus on regression: Bayesian and Frequentist Regression Methods

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One of the most lucid expositions of Bayesian Thinking can be found in "Bayes' Rule" by Jim Stone. The same book comes in a several versions, with accompanying R, Python and MATLAB code.

http://jim-stone.staff.shef.ac.uk/BookBayes2012/BayesRuleBookMain.html

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