By Martin A. Tanner

**From the reviews**: the aim of the publication lower than evaluation is to offer a survey of tools for the Bayesian or likelihood-based research of information. the writer distinguishes among varieties of equipment: the saw info tools and the knowledge augmentation ones. The saw info tools are utilized on to the chance or posterior density of the saw info. the information augmentation tools utilize the unique "missing" information constitution of the matter. They depend on an augmentation of the knowledge which simplifies the possibility or posterior density. #*Zentralblatt für **Mathematik*#

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**Extra resources for Tools for Statistical Inference: Observed Data and Data Augmentation Methods**

**Example text**

The augmented data are given by such that Xl +X2 = 125 X3 = Y2 i and 32 X5 = Y4 Notice that the observed posterior (under a flat prior) is proportional to (2 + 0)"(1- O)W3+no~, while the augmented posterior (under a flat prior) is proportional to 0'f2+'fS(1 _ 0)'fS+'f4. By working with the augmented posterior we realize a simplification in functional form. For this genetic linkage model note that Q(O, Oi) = E{(X2 + X5) log(O) + (X3 + X4) log(1 - O)IOi, Y}, where p(ZIOi, Y) is the binomial distribution with n = 125 and p = Oi /«(Ji Q«(J,Oi) simplifies to and is linear in the latent data.

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Rubin, Journal of the Royal Statistical Society, B, 39, 24-25. G. A. (1990) "A Monte Culo Implementation of the EM Algorithm and the Poor Man's Data Augmentation Algorithms", Journal of the AmeriCan Statistical Associatjon, 85, 699-704. J. (1983). ic§, 11,95-103. V. The Data Augmentation Algorithm A. Introduction and Motivation Analogous to the EM algorithm, the Data Augmentation algorithm exploits the simplicity of the posterior distribution of the parameter given the augmented data. In contrast to the EM algorithm, the present goal is obtain the entire posterior distribution, not just the maximizer and the curvature at the maximizer.