Springer Series in Statistics

Tools for Statistical Inference

Methods for the Exploration of Posterior Distributions and Likelihood Functions

Authors: Tanner, Martin A.

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About this Textbook

This book provides a unified introduction to a variety of computational algorithms for likelihood and Bayesian inference. In this second edition, I have attempted to expand the treatment of many of the techniques disĀ­ cussed, as well as include important topics such as the Metropolis algorithm and methods for assessing the convergence of a Markov chain algorithm. 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), experience with condiĀ­ tional inference at the level of Cox and Snell (1989) and exposure to statistical models as found in McCullagh and Neider (1989). I have chosen not to present the proofs of convergence or rates of convergence since these proofs may require substantial background in Markov chain theory which is beyond the scope ofthis 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 last five years. I have attempted to identify key references - though due to the volatility of the field some work may have been missed.

Reviews

"Extremely useful as an introduction to an interesting, developing field in statistics... I highly recommend it for the library of every well-informed statistician."
(Journal of the Am. Statistical Assoc.)

Table of contents (6 chapters)

  • Introduction

    Tanner, Martin A.

    Pages 1-8

  • Normal Approximations to Likelihoods and to Posteriors

    Tanner, Martin A.

    Pages 9-19

  • Nonnormal Approximations to Likelihoods and to Posteriors

    Tanner, Martin A.

    Pages 20-37

  • The EM Algorithm

    Tanner, Martin A.

    Pages 38-57

  • The Data Augmentation Algorithm

    Tanner, Martin A.

    Pages 58-101

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-1-4684-0192-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Tools for Statistical Inference
Book Subtitle
Methods for the Exploration of Posterior Distributions and Likelihood Functions
Authors
Series Title
Springer Series in Statistics
Copyright
1993
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York, Inc.
eBook ISBN
978-1-4684-0192-9
DOI
10.1007/978-1-4684-0192-9
Series ISSN
0172-7397
Edition Number
2
Additional Information
Originally published as volume 67 in the series: Lecture Notes in Statistics
Topics