An excellent introduction (and much more) to Bayes and Inference. Very well written and ties together several bits of statistics quite nicely eg relationships between binomial, Poisson, Gaussian distributions, student-t, chi-squared distributions; why the estimate for standard deviation divides by (N-1) instead of N, and so on. It does get pretty technical so would hold the interest of a practitioner of statistics, I think. ( )

This book not only is a good book to learn Bayesian statistics from, but it's also a great reference for the subject as well. Taking a very hands-on approach, the concepts and philosophy of Bayesian statistical analysis are clearly presented through lucid explanations and an abundance of well-chosen examples. In the second edition, there is also a significant portion of the book dedicated to algorithmic implementation of Bayesian inference schemes; and this material is accompanied by C source code snippets to really solidify the ideas behind the algorithms. My one issue with this book is that I wish more pages had been dedicated to discussing MCMC (Markov Chain Monte-Carlo) algorithms for sampling posterior distributions. Indeed, adaptive MCMC algorithms represent the majority of sampling algorithms implemented when it comes to sampling analytically unknown posterior distributions, but these are scarcely mentioned in this book.

Overall, I think this is the best book out there in regards to explaining how to actually implement Bayesian analytical techniques on scientific or engineering data. ( )