Tools for Statistical Inference

1. Front Matter

   Pages i-viii

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2. Introduction

   • Martin A. Tanner

   Pages 1-13

3. Normal Approximations to Likelihoods and to Posteriors

   • Martin A. Tanner

   Pages 14-39

4. Nonnormal Approximations to Likelihoods and Posteriors

   • Martin A. Tanner

   Pages 40-63

5. The EM Algorithm

   • Martin A. Tanner

   Pages 64-89

6. The Data Augmentation Algorithm

   • Martin A. Tanner

   Pages 90-136

7. Markov Chain Monte Carlo: The Gibbs Sampler and the Metropolis Algorithm

   • Martin A. Tanner

   Pages 137-192

8. Back Matter

   Pages 193-208

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This book provides a unified introduction to a variety of computational algorithms for Bayesian and likelihood inference. In this third edition, I have attempted to expand the treatment of many of the techniques discussed. I have added some new examples, as well as included recent results. Exercises have been added at the end of each chapter. Prerequisites for this book include an understanding of mathematical statistics at the level of Bickel and Doksum (1977), some understanding of the Bayesian approach as in Box and Tiao (1973), some exposure to statistical models as found in McCullagh and NeIder (1989), and for Section 6. 6 some experience with condi­ tional inference at the level of Cox and Snell (1989). I have chosen not to present proofs of convergence or rates of convergence for the Metropolis algorithm or the Gibbs sampler since these may require substantial background in Markov chain theory that is beyond the scope of this book. However, references to these proofs are given. There has been an explosion of papers in the area of Markov chain Monte Carlo in the past ten years. I have attempted to identify key references-though due to the volatility of the field some work may have been missed.

• Bayesian inference
• Gibbs sampler
• Likelihood
• Resampling
• algorithms
• expectation–maximization algorithm
• observed data

• Department of Statistics, Northwestern University, Evanston, USA

  Martin A. Tanner

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