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Tools for Statistical Inference

Methods for the Exploration of Posterior Distributions and Likelihood Functions

  • Textbook
  • © 1993

Overview

Authors:
  1. Martin A. Tanner

    1. Rochester, USA

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Part of the book series: Springer Series in Statistics (SSS)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-ix
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  2. Introduction

    • Martin A. Tanner
    Pages 1-8

  3. Normal Approximations to Likelihoods and to Posteriors

    • Martin A. Tanner
    Pages 9-19

  4. Nonnormal Approximations to Likelihoods and to Posteriors

    • Martin A. Tanner
    Pages 20-37

  5. The EM Algorithm

    • Martin A. Tanner
    Pages 38-57

  6. The Data Augmentation Algorithm

    • Martin A. Tanner
    Pages 58-101

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

    • Martin A. Tanner
    Pages 102-146

  8. Back Matter

    Pages 147-157
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Keywords

About this book

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 dis­ 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 condi­ 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.)

Authors and Affiliations

  • Rochester, USA

    Martin A. Tanner

Bibliographic Information

  • Book Title: Tools for Statistical Inference

  • Book Subtitle: Methods for the Exploration of Posterior Distributions and Likelihood Functions

  • Authors: Martin A. Tanner

  • Series Title: Springer Series in Statistics

  • DOI: https://doi.org/10.1007/978-1-4684-0192-9

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 1993

  • eBook ISBN: 978-1-4684-0192-9Published: 06 December 2012

  • Series ISSN: 0172-7397

  • Series E-ISSN: 2197-568X

  • Edition Number: 2

  • Additional Information: Originally published as volume 67 in the series: Lecture Notes in Statistics

  • Topics: Applications of Mathematics

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