Bayesian Statistics: An Introduction

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John Wiley & Sons, Jun 25, 2012 - Mathematics - 488 pages
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Bayesian Statistics is the school of thought that combines priorbeliefs with the likelihood of a hypothesis to arrive at posteriorbeliefs. The first edition of Peter Lee’s book appeared in1989, but the subject has moved ever onwards, with increasingemphasis on Monte Carlo based techniques.

This new fourth edition looks at recent techniques such asvariational methods, Bayesian importance sampling, approximateBayesian computation and Reversible Jump Markov Chain Monte Carlo(RJMCMC), providing a concise account of the way in which theBayesian approach to statistics develops as well as how itcontrasts with the conventional approach. The theory is built upstep by step, and important notions such as sufficiency are broughtout of a discussion of the salient features of specificexamples.

This edition:

  • Includes expanded coverage of Gibbs sampling, including morenumerical examples and treatments of OpenBUGS, R2WinBUGS andR2OpenBUGS.
  • Presents significant new material on recent techniques such asBayesian importance sampling, variational Bayes, ApproximateBayesian Computation (ABC) and Reversible Jump Markov Chain MonteCarlo (RJMCMC).
  • Provides extensive examples throughout the book to complementthe theory presented.
  • Accompanied by a supporting website featuring new material andsolutions.

More and more students are realizing that they need to learnBayesian statistics to meet their academic and professional goals.This book is best suited for use as a main text in courses onBayesian statistics for third and fourth year undergraduates andpostgraduate students.


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Bayesian inference for the normal distribution
Hypothesis testing 4 1 Hypothesis testing 4 2 Onesided hypothesis tests 4 3 Lindleys method 4 4 Point or sharpnull hypotheses with prior information
Twosample problems
3Regression andthebivariate normalmodel 6 4Conjugate
Othertopics 7 1 The likelihoodprinciple 7 2 The stopping rule principle
2TheEM algorithm 9 3Data augmentation by Monte Carlo 9 4TheGibbs sampler
Some approximate methods
Common statistical distributions

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About the author (2012)

Peter Lee, Department of Mathematics & Formerly Provost of Wentworth College, University of York.

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