[_0w8t]

For me the best so far book on Bayesian probability was "Probability Theory: The Logic of Science: Principles and Elementary Applications" by E. T. Jaynes.

The book starts from the deduction of Bayesian theorem from the first principles of logic and shows its applications to a wide range of topics. There is thorough discussion of various "paradoxes" and the author sharply criticizes the frequentist statistics. In addition there is a lot of historical references.

[CalChris]

Probability Theory is available as a PDF.

http://www.med.mcgill.ca/epidemiology/hanley/bios601/Gaussia...

[rtehfm]

Thanks. I was about to buy the book on Amazon for ~$90 but at least now I can give it a read first to see if it's worth, for me at least, buying.

[vowelless]

Great book. Unfortunately Jaynes passed away before he could finish it. Still, a great take on probability theory.

[xelxebar]

I came here to recommend this book too! It's a text that definitely allows one to go as deep as they wish very fleshed out references, a good appendix, and lots of comments on directions that can be explored more deeply.

It's a book I'm happy to have in dead tree form on my shelf.