Tools for Statistical Inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions (Springer Series in Statistics) [Hardcover]

Martin A. Tanner (Author)

Book Description

Publication Date: June 26, 1996 | ISBN-10: 0387946888 | ISBN-13: 978-0387946887 | Edition: 3rd

A unified introduction to a variety of computational algorithms for likelihood and Bayesian inference. This third edition expands the discussion of many of the techniques presented, and includes additional examples as well as exercise sets at the end of each chapter.

Product Details

• Hardcover: 220 pages
• Publisher: Springer; 3rd edition (June 26, 1996)
• Language: English
• ISBN-10: 0387946888
• ISBN-13: 978-0387946887
• Product Dimensions: 9.3 x 6.3 x 0.8 inches
• Shipping Weight: 1.3 pounds (View shipping rates and policies)
• Average Customer Review: 3.8 out of 5 stars  See all reviews (5 customer reviews)
• Amazon Best Sellers Rank: #1,169,690 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

24 of 24 people found the following review helpful:

4.0 out of 5 stars something a little different but interesting, January 23, 2008

By 

Michael R. Chernick "statman31147" (Holland PA) - See all my reviews
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This review is from: Tools for Statistical Inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions (Springer Series in Statistics) (Hardcover)

This is a very well written text that is a particularly good reference on algorithms for the professional statistician. A nice feature is that it is concise and yet thorough. Many important problems in statistics are covered and presented through the deterministic and Monte Carlo techniques. Topics covered include the item response model, missing data and Bayesian methods. Most algorithms used to find maxima of posterior distributions can also be employed for maximizing likelihood. So those preferring classical inference can get a lot out of this book as well as the Bayesians.
The orientation is toward the Bayesian approach however, with good coverage of prior and posterior distributions, conjugate priors and Bayesian Hierarchical Models. The last chapter on Markov Chain Monte Carlo methods is mostly used for Bayesian inference.

This is a great reference source but can also be used in a graduate level course on mathematical statistics, probably as a supplemental text. There are many useful exercises in this edition. The book is fairly advanced and presupposes an introduction to mathematical statistics at the level of the text by Bickel and Doksum. It also assumes that the reader has had some introduction to Bayesian methods but only at the level of, say, Box and Tiao's text. It does not assume any knowledge of stochastic processes including Markov chains.

Convergence properties for the Markov Chain Monte Carlo algorithms (MCMC) are crucial to their success. Elements of discrete Markov chains are introduced in chapter 6 to make the algorithms understandable, but proof of convergence are avoided because they would involve a more detailed account of Markov chain theory.

Tanner provides a good list of the references that were available in 1996. The research in MCMC methods is continuing to be intense and so there are many good references that have appeared since the publication of this book. Robert and Casella (1999) provides a more detailed and more current treatment but even that book is a couple of years dated.

The EM and data augmentation algorthms are used for problems that are classified as missing data problems. The data may be missing as in a survey where particular questions are not answered by the respondents or it could be censored data as in a medical study or clinical trial. The censored data problem is illustrated by Tanner using the Stanford Heart Transplant data. Mixture models are also handled via these algorithms since the identification of the component that the observation belongs to can be viewed as missing data.

Tanner demonstrates a wide variety of techniques to handle many important problems and he illustrates them on real data. It is nice to have all of this compactly written in just 200 pages!

11 of 13 people found the following review helpful:

4.0 out of 5 stars A brief reference book of EM algorithm, MC methods, etc. Recommended!, September 12, 2005

By 

supercutepig (USA) - See all my reviews

This review is from: Tools for Statistical Inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions (Springer Series in Statistics) (Hardcover)

We used this book as a main reference in a seminar of several weeks. Totally, it is well written, without superfluous words.

[1] It describes the contents of Expectation Maximization (EM) algorithm, data augmentation, etc precisely.
[2] It is not too thick to make reading a boring experience.
[3] Graduate level textbook or reference book.

1 of 3 people found the following review helpful:

4.0 out of 5 stars The EM Algorithm, February 27, 2006

By 

Thomas R. Fielden (Portland, OR USA) - See all my reviews
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This review is from: Tools for Statistical Inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions (Springer Series in Statistics) (Hardcover)

I'm working through chapter 4 for a statistics course. I find that the book doesn't leave any holes to be filled, but begs certain important concepts to be called out. At least the concepts appear to all be present.