Martin A. Tanner

Tools for Statistical Inference (eBook, PDF)

Observed Data and Data Augmentation Methods

• Format: PDF

Produktbeschreibung

From the reviews: The purpose of the book under review is to give a survey of methods for the Bayesian or likelihood-based analysis of data. The author distinguishes between two types of methods: the observed data methods and the data augmentation ones. The observed data methods are applied directly to the likelihood or posterior density of the observed data. The data augmentation methods make use of the special "missing" data structure of the problem. They rely on an augmentation of the data which simplifies the likelihood or posterior density. #Zentralblatt für Mathematik#

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Produktdetails

• Verlag: Springer New York
• Seitenzahl: 110
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781468405101
• Artikelnr.: 44176618

Inhaltsangabe

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.