Tools for Statistical Inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions / Edition 3

by Martin A. Tanner

Overview

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

ISBN-13:	9781461284710
Publisher:	Springer New York
Publication date:	09/27/2011
Series:	Springer Series in Statistics
Edition description:	3rd ed. 1996. Softcover reprint of the original 3rd ed. 1996
Pages:	208
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

1. Introduction.- Exercises.- 2. Normal Approximations to Likelihoods and to Posteriors.- 2.1. Likelihood/Posterior Density.- 2.2. Specification of the Prior.- 2.3. Maximum Likelihood.- 2.4. Normal-Based Inference.- 2.5. The—-Method (Propagation of Errors).- 2.6. Highest Posterior Density Regions.- Exercises.- 3. Nonnormal Approximations to Likelihoods and Posteriors.- 3.1. Numerical Integration.- 3.2. Posterior Moments and Marginalization Based on Laplace’s Method.- 3.3. Monte Carlo Methods.- Exercises.- 4. The EM Algorithm.- 4.1. Introduction.- 4.2. Theory.- 4.3. EM in the Exponential Family.- 4.4. Standard Errors in the Context of EM.- 4.5. Monte Carlo Implementation of the E-Step.- 4.6. Acceleration of EM (Louis’ Turbo EM).- 4.7. Facilitating the M-Step.- Exercises.- 5. The Data Augmentation Algorithm.- 5.1. Introduction and Motivation.- 5.2. Computing and Sampling from the Predictive Distribution.- 5.3. Calculating the Content and Boundary of the HPD Region.- 5.4. Remarks on the General Implementation of the Data Augmentation Algorithm.- 5.5. Overview of the Convergence Theory of Data Augmentation.- 5.6. Poor Man’s Data Augmentation Algorithms.- 5.7. Sampling/Importance Resampling (SIR).- 5.8. General Imputation Methods.- 5.9. Further Importance Sampling Ideas.- 5.10. Sampling in the Context of Multinomial Data.- Exercises.- 6. Markov Chain Monte Carlo: The Gibbs Sampler and the Metropolis Algorithm.- 6.1. Introduction to the Gibbs Sampler.- 6.2. Examples.- 6.3. Assessing Convergence of the Chain.- 6.4. The Griddy Gibbs Sampler.- 6.5. The Metropolis Algorithm.- 6.6. Conditional Inference via the Gibbs Sampler.- Exercises.- References.