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Essential Bayesian Models

by: Rao; Dey

Essential Bayesian Models

by: Rao; Dey

ISBN 13:
9780444537324
ISBN 10:
0444537325
Format: Hardcover
Copyright: 12/30/2010
Publisher: Elsevier Science

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Summary

This accessible reference includes selected contributions from Bayesian Thinking - Modeling and Computation, Volume 25 in the Handbook of Statistics Series, with a focus on key methodologies and applications for Bayesian models and computation. It describes parametric and nonparametric Bayesian methods for modeling, and how to use modern computational methods to summarize inferences using simulation. The book covers a wide range of topics including objective and subjective Bayesian inferences, with a variety of applications in modeling categorical, survival, spatial, spatiotemporal, Epidemiological, small area and micro array data. Aids critical thinking on causal effects Provides simulation based computing techniques Covers Bioinformatics and Biostatistics

List of Contributors	p. xi
Bayesian Inference for Causal Effects	p. 1
Causal inference primitives	p. 1
A brief history of the potential outcomes framework	p. 5
Models for the underlying data - Bayesian inference	p. 7
Complications	p. 12
Model Selection and Hypothesis Testing based on Objective Probabilities and Bayes Factors	p. 17
Introduction	p. 17
Objective Bayesian model selection methods	p. 23
More general training samples	p. 45
Prior probabilities	p. 47
Conclusions	p. 47
Acknowledgements	p. 48
Bayesian Model Checking and Model Diagnostics	p. 53
Introduction	p. 53
Model checking overview	p. 54
Approaches for checking if the model is consistent with the data	p. 55
Posterior predictive model checking techniques	p. 58
Application 1	p. 62
Application 2	p. 63
Conclusions	p. 72
Bayesian Nonparametric Modeling and Data Analysis: An Introduction	p. 75
Introduction to Bayesian nonparametrics	p. 75
Probability measures on spaces of probability measures	p. 77
Illustrations	p. 87
Concluding remarks	p. 102
Some Bayesian Nonparametric Models	p. 107
Introduction	p. 107
Random distribution functions	p. 109
Mixtures of Dirichlet processes	p. 112
Random variate generation for NTR processes	p. 114
Sub-classes of random distribution functions	p. 120
Hazard rate processes	p. 126
Polya trees	p. 130
Beyond NTR processes and Polya trees	p. 134
Bayesian Modeling in the Wavelet Domain	p. 143
Introduction	p. 143
Bayes and wavelets	p. 145
Other problems	p. 160
Acknowledgements	p. 162
Bayesian Methods for Function Estimation	p. 167
Introduction	p. 167
Priors on infinite-dimensional spaces	p. 168
Consistency and rates of convergence	p. 177
Estimation of cumulative probability distribution	p. 187
Density estimation	p. 189
Regression function estimation	p. 195
Spectral density estimation	p. 198
Estimation of transition density	p. 200
Concluding remarks	p. 201
MCMC Methods to Estimate Bayesian Parametric Models	p. 209
Motivation	p. 209
Bayesian ingredients	p. 210
Bayesian recipe	p. 210
How can the Bayesian pie burn	p. 211
MCMC methods	p. 212
The perfect Bayesian pie: How to avoid "burn-in" issues	p. 225
Conclusions	p. 226
Bayesian Computation: From Posterior Densities to Bayes Factors, Marginal Likelihoods, and Posterior Model Probabilities	p. 231
Introduction	p. 231
Posterior density estimation	p. 232
Marginal posterior densities for generalized linear models	p. 241
Savage-Dickey density ratio	p. 243
Computing marginal likelihoods	p. 244
Computing posterior model probabilities via informative priors	p. 245
Concluding remarks	p. 249
Bayesian Modelling and Inference on Mixtures of Distributions	p. 253
Introduction	p. 253
The finite mixture framework	p. 254
The mixture conundrum	p. 260
Inference for mixture models with known number of components	p. 274
Inference for mixture models with unknown number of components	p. 290
Extensions to the mixture framework	p. 294
Acknowledgements	p. 296
Variable Selection and Covariance Selection in Multivariate Regression Models	p. 301
Introduction	p. 301
Model description	p. 303
Sampling scheme	p. 308
Real data	p. 309
Simulation study	p. 323
Summary	p. 332
Dynamic Models	p. 335
Model structure, inference and practical aspects	p. 335
Markov Chain Monte Carlo	p. 346
Sequential Monte Carlo	p. 354
Extensions	p. 361
Acknowledgements	p. 365
Elliptical Measurement Error Models - A Bayesian Approach	p. 371
Introduction	p. 371
Elliptical measurement error models	p. 373
Diffuse prior distribution for the incidental parameters	p. 375
Dependent elliptical MEM	p. 376
Independent elliptical MEM	p. 381
Application	p. 388
Acknowledgements	p. 389
Bayesian Sensitivity Analysis in Skew-Elliptical Models	p. 391
Introduction	p. 391
Definitions and properties of skew-elliptical distributions	p. 394
Testing of asymmetry in linear regression model	p. 401
Simulation results	p. 407
Conclusions	p. 408
Acknowledgements	p. 409
Bayesian Methods for DNA Microarray Data Analysis	p. 415
Introduction	p. 415
Review of microarray technology	p. 416
Statistical analysis of microarray data	p. 418
Bayesian models for gene selection	p. 419
Differential gene expression analysis	p. 432
Bayesian clustering methods	p. 436
Regression for grossly overparametrized models	p. 439
Concluding remarks	p. 440
Acknowledgements	p. 440
Bayesian Biostatistics	p. 445
Introduction	p. 445
Correlated and longitudinal data	p. 446
Time to event data	p. 450
Nonlinear modeling	p. 454
Model averaging	p. 456
Bioinformatics	p. 458
Discussion	p. 459
Innovative Bayesian Methods for Biostatistics and Epidemiology	p. 465
Introduction	p. 465
Meta-analysis and multicentre studies	p. 467
Spatial analysis for environmental epidemiology	p. 469
Adjusting for mismeasured variables	p. 471
Adjusting for missing data	p. 474
Sensitivity analysis for unobserved confounding	p. 476
Ecological inference	p. 478
Bayesian model averaging	p. 481
Survival analysis	p. 483
Case-control analysis	p. 485
Bayesian applications in health economics	p. 487
Discussion	p. 488
Modeling and Analysis for Categorical Response Data	p. 495
Introduction	p. 495
Binary responses	p. 500
Ordinal response data	p. 505
Sequential ordinal model	p. 508
Multivariate responses	p. 510
Longitudinal binary responses	p. 517
Longitudinal multivariate responses	p. 522
Conclusion	p. 524
Bayesian Methods and Simulation-Based Computation for Contingency Tables	p. 527
Motivation for Bayesian methods	p. 527
Advances in simulation-based Bayesian calculation	p. 527
Early Bayesian analyses of categorical data	p. 528
Bayesian smoothing of contingency tables	p. 530
Bayesian interaction analysis	p. 534
Bayesian tests of equiprobability and independence	p. 537
Bayes factors for GLM's with application to log-linear models	p. 539
Use of BIC in sociological applications	p. 542
Bayesian model search for loglinear models	p. 542
The future	p. 545
Teaching Bayesian Thought to Nonstatisticians	p. 549
Introduction	p. 549
A brief literature review	p. 550
Commonalities across groups in teaching Bayesian methods	p. 550
Motivation and conceptual explanations: One solution	p. 552
Conceptual mapping	p. 554
Active learning and repetition	p. 554
Assessment	p. 555
Conclusions	p. 557
Subject Index	p. 559
Table of Contents provided by Ingram. All Rights Reserved.

Amazon no longer offers textbook rentals. We do!

Essential Bayesian Models

Essential Bayesian Models

9780444537324

0444537325

Summary

Table of Contents

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