This book is intended to have three roles and to serve three associated audiences： anintroductory text on Bayesian inference starting from first principles， a graduate text oneffective current approaches to Bayesian modeling and computation in statistics and relatedfields， and a handbook of Bayesian methods in applied statistics for general users of andresearchers in applied statistics. Although introductory in its early sections， the book isdefinitely not elementary in the sense of a first text in statistics. The mathematics usedin our book is basic probability and statistics， elementary calculus， and linear algebra. Areview of probability notation is given in Chapter 1 along with a more detailed list of topicsassumed to have been studied. The practical orientation of the book means that the reader'sprevious experience in probability， statistics， and linear algebra should ideally have includedstrong computational components.
　　To write an introductory text alone would leave many readers with only a taste of theconceptual elements but no guidance for venturing into genuine practical applications， be-yond those where Bayesian methods agree essentially with standard non-Bayesian analyses.On the other hand， we feel it would be a mistake to present the advanced methods with-out first introducing the basic concepts from our data-analytic perspective. Furthermore，due to the nature of applied statistics， a text on current Bayesian methodology would beincomplete without a variety of worked examples drawn from real applications. To avoidcluttering the main narrative， there are bibliographic notes at the end of each chapter andreferences at the end of the book.