Get Bayesian Missing Data Problems: EM, Data Augmentation and PDF

By Ming T. Tan

ISBN-10: 142007749X

ISBN-13: 9781420077490

Bayesian lacking facts difficulties: EM, info Augmentation and Noniterative Computation provides suggestions to lacking information difficulties via specific or noniterative sampling calculation of Bayesian posteriors. The tools are in response to the inverse Bayes formulae found by way of one of many writer in 1995. utilizing the Bayesian method of very important real-world difficulties, the authors concentrate on targeted numerical recommendations, a conditional sampling method through info augmentation, and a noniterative sampling strategy through EM-type algorithms.

After introducing the lacking info difficulties, Bayesian technique, and posterior computation, the e-book succinctly describes EM-type algorithms, Monte Carlo simulation, numerical thoughts, and optimization equipment. It then supplies specific posterior options for difficulties, resembling nonresponses in surveys and cross-over trials with lacking values. It additionally offers noniterative posterior sampling suggestions for difficulties, similar to contingency tables with supplemental margins, aggregated responses in surveys, zero-inflated Poisson, capture-recapture versions, combined results types, right-censored regression version, and restricted parameter types. The textual content concludes with a dialogue on compatibility, a primary factor in Bayesian inference.

This ebook bargains a unified remedy of an array of statistical difficulties that contain lacking information and restricted parameters. It indicates how Bayesian strategies should be beneficial in fixing those problems.

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Additional info for Bayesian Missing Data Problems: EM, Data Augmentation and Noniterative Computation (Chapman & Hall/CRC Biostatistics Series)

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7 Let xi > 0, pi > 0, i = 1, . . , d, and di=1 pi = 1, then a) di=1 pi log2 xi ≤ log2 ( di=1 pi xi ); b) di=1 pi log2 p−1 i ≤ log2 d. v. ) © 2010 by Taylor and Francis Group, LLC 34 1. v. X defined on X have pdf f (x), show that SE(X) is maximal iff f is the uniform distribution on X . ’s. Prove the following statements: a) SE(X|Y ) ≤ SE(X); b) SE(X, Y |Z) = SE(X|Z) + SE(Y |X, Z); c) The mutual information of X and Y satisfies M(X, Y ) = SE(X) − SE(X|Y ) = SE(Y ) − SE(Y |X). 10 Convexity and Jensen’s inequality.

Xd ) is known and relatively easy to simulate. Choose a starting point (0) (0) X (0) = (X1 , . . , Xd ) and set t = 0, the Gibbs sampling iterates the following loop: (t+1) ∼ f (X1 |X2 , . . , Xd ); (t+1) ∼ f (X2 |X1 ··· (t+1) ∼ f (Xd |X1 • Draw X1 • Draw X2 ··· ··· • Draw Xd (t) (t) (t+1) , X3 , . . , Xd ); (t) (t) (t+1) , . . , Xd−1 ). (t+1) Gelfand & Smith (1990) show that under mild conditions, the vector sequence {X (t) }∞ t=1 has a stationary distribution F (·). Schervish & Carlin (1992) provide a sufficient condition that guarantees geometric convergence.

14) respectively. 14) is called the Dirichlet multinomial density (cf. 4): y ∼ DMultinomialn (N, a), © 2010 by Taylor and Francis Group, LLC y ∈ Tn (N ). 14) is a mixture of multinomial distribution with rates, θ, and it follows a Dirichlet distribution . Therefore, the Dirichlet multinomial distribution is a robust alternative to the multinomial distribution. 2 Nuisance parameters A major difficulty with the classical likelihood approach is with nuisance parameters. Let θ = (θ1 , θ−1 ), where θ1 is the parameter of interest and θ−1 denotes all but the first component.

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Bayesian Missing Data Problems: EM, Data Augmentation and Noniterative Computation (Chapman & Hall/CRC Biostatistics Series) by Ming T. Tan


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