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Bayesian Data Analysis, Second Edition (Chapman & Hall/CRC Texts in Statistical Science)

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This book is intended to have three roles and to serve three associated audiences: an introductory text on Bayesian inference star ting from first principles, a graduate text on effective current approaches to Bayesian modeling and computation in statistics and related fields, and a handbook of Bayesian meth ods in applied statistics for general users of and researchers in applied statistics. Although introductory in its early sections, the b ook is definitely not elementary in the sense of a first text in statistics. The mathematics used in our book is basic probability and statistics, elementary calculus, and linea r algebra. A review of probability notation is given in Chapter 1 along with a more detaile d list of topics assumed to have been studied. The practical orientation of the book means that the reader’s previous experience in pr obability, statistics, and linear algebra should ideally have included stro ng computational components.

To write an introductory text alone would l eave many readers with only a taste of the conceptual elements but no guidance for venturing into genuine practical applications, beyond those where Bayesian methods agree essentially with standard non-Bayesian analyses. On the other hand, given the continuing scarcity of introductions to applied Bayesian statistics either in books or in statistical education, we feel it would be a mistake to present the advanced methods without 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 be incomplete without a variety of worked examples drawn from real a pplications. To avoid cluttering the main narrative, there are bibliographic notes at the end of each chapter and references at the end of the book.

Examples of real statistical analyses ar e found throughout the book, and we hope thereby to give a genuine applied flavor to the entire development. Indeed, given the conceptual simplicity of the Bayesian approach, it is only in the intricacy of specific applications that novelty arises. Non-Bayesi an approaches to inference have dominate d statistical theory and practice for most of the past century, but the last two decades or so have seen a reemergence of th e Bayesian approach. This ha s been driven more by the availability of new computational techniques than by what many would see as the philosophical and logical advant ages of Bayesian thinking.

We hope that the publication of this book will enhance the spread of ideas that are currently trickling through the scientific li terature. The models and methods developed recently in this field have yet to reach thei r largest possible audien ce, partly because the results are scattered in various journals and p roceedings volumes. We hope that this book will help a new generation of statisticians and users of statistics to solve complicated problems with greater understanding.
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