Jim Press has produced a second edition to a book that had a different title but most of the same content. I have reviewed the earlier edition for amazon. So I will only point out the additions. In the past twenty years there has been a revolution in Bayesian statistics due to the Markov Chain Monte Carlo algorithms (MCMC) being rediscovered and applied to Bayesian hierarchical modeling. The algorithm from the 1950s goes by the name Metropolis-Hastings for the two physicists who first published it. Another algorithm that is a modification of Metropolis-Hastings is called the Gibbs Sampler.
The only major piece missing from the earlier work was the coverage of the Bayesian Hierarchical models which were too difficult to solve in the past. But today the computers are fast enough to make it possible to compute the posteriori distributions through MCMC. That is the most important addition to the text. Also added is Bayesian factor analysis, a topic not covered in most books on Bayesian statistics.
The first edition of this text included mostly univariate statistics. Professor Press has also written a book on multivariate Bayesian methods and has expanded many sections in this book to incorporate multivariate problems. Factor analysis and Classification models are two examples.
As with all his books Professor Press writes clearly, covers the basics and presents many practical applications and examples.