Tools for Statistical Inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions (Springer Series in Statistics)

Tanner, Martin A. A.

ISBN 10: 1461284716 / ISBN 13: 9781461284710

Editore: Springer, 2011

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Dati bibliografici

• Titolo: Tools for Statistical Inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions (Springer Series in Statistics)
• Editore: Springer
• Data di pubblicazione: 2011
• Lingua: Inglese
• ISBN 10: 1461284716
• ISBN 13: 9781461284710
• Rilegatura: Brossura
• Edizione: terza edizione
• Condizione: New

Descrizione articolo

Riassunto

This book provides a unified introduction to a variety of computational algorithms for likelihood and Bayesian inference. The third edition expands the discussion of many of the techniques discussed, includes additional examples, and adds exercise sets at the end of each chapter.

Contenuti

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.