Tools for Statistical Inference
Observed Data and Data Augmentation Methods
Published on 6. December 2012
VI, 110 pages
978-1-4684-0510-1 (ISBN)
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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. #
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Mathematik
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03/1993
Springer
€85.55
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Content
I. Introduction.- A. Problems.- B. Techniques.- References.- II. Observed Data Techniques-Normal Approximation.- A. Likelihood/Posterior Density.- B. Maximum Likelihood.- C. Normal Based Inference.- D. The Delta Method.- E. Significance Levels.- References.- III. Observed Data Techniques.- A. Numerical Integration.- B. Litplace Expansion.- C. Monte Carlo Methods.- IV. The EM Algorithm.- A. Introduction.- B. Theory.- C. EM in the Exponential Family.- D. Standard Errors.- E. Monte Carlo Implementation of the E-Step.- F. Acceleration of EM.- References.- V. Data Augmentation.- A. Introduction.- B. Predictive Distribution.- C. HPD Region Computations.- D. Implementation.- E. Theory.- F. Poor Man's Data Augmentation.- G. SIR.- H. General Imputation Methods.- I. Data Augmentation via Importance Sampling.- J. Sampling in the Context of Multinomial Data.- VI. The Gibbs Sampler.- A. Introduction.- B. Examples.- C. The Griddy Gibbs Sampler.
