The Resource Monte Carlo Methods in Bayesian Computation, by Ming-Hui Chen, Qi-Man Shao, Joseph G. Ibrahim, (electronic resource)

Monte Carlo Methods in Bayesian Computation, by Ming-Hui Chen, Qi-Man Shao, Joseph G. Ibrahim, (electronic resource)

Label
Monte Carlo Methods in Bayesian Computation
Title
Monte Carlo Methods in Bayesian Computation
Statement of responsibility
by Ming-Hui Chen, Qi-Man Shao, Joseph G. Ibrahim
Creator
Contributor
Author
Author
Subject
Language
  • eng
  • eng
Summary
Sampling from the posterior distribution and computing posterior quanti­ ties of interest using Markov chain Monte Carlo (MCMC) samples are two major challenges involved in advanced Bayesian computation. This book examines each of these issues in detail and focuses heavily on comput­ ing various posterior quantities of interest from a given MCMC sample. Several topics are addressed, including techniques for MCMC sampling, Monte Carlo (MC) methods for estimation of posterior summaries, improv­ ing simulation accuracy, marginal posterior density estimation, estimation of normalizing constants, constrained parameter problems, Highest Poste­ rior Density (HPD) interval calculations, computation of posterior modes, and posterior computations for proportional hazards models and Dirichlet process models. Also extensive discussion is given for computations in­ volving model comparisons, including both nested and nonnested models. Marginal likelihood methods, ratios of normalizing constants, Bayes fac­ tors, the Savage-Dickey density ratio, Stochastic Search Variable Selection (SSVS), Bayesian Model Averaging (BMA), the reverse jump algorithm, and model adequacy using predictive and latent residual approaches are also discussed. The book presents an equal mixture of theory and real applications
Member of
http://library.link/vocab/creatorName
Chen, Ming-Hui
Dewey number
519.2
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
  • d4hwQIV0bN0
  • GeEuH-nqN9s
  • mZqFx8V_C0U
Image bit depth
0
Language note
English
LC call number
  • QA273.A1-274.9
  • QA274-274.9
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
  • Shao, Qi-Man.
  • Ibrahim, Joseph G.
Series statement
Springer Series in Statistics,
http://library.link/vocab/subjectName
  • Distribution (Probability theory
  • Mathematical statistics
  • Statistics
  • Probability Theory and Stochastic Processes
  • Statistical Theory and Methods
  • Statistics for Life Sciences, Medicine, Health Sciences
  • Statistics and Computing/Statistics Programs
Label
Monte Carlo Methods in Bayesian Computation, by Ming-Hui Chen, Qi-Man Shao, Joseph G. Ibrahim, (electronic resource)
Instantiates
Publication
Note
"With 32 illustrations."
Antecedent source
mixed
Bibliography note
Includes bibliographical references and indexes
Carrier category
online resource
Carrier category code
cr
Color
not applicable
Content category
text
Content type code
txt
Contents
1 Introduction -- 1.1 Aims -- 1.2 Outline -- 1.3 Motivating Examples -- 1.4 The Bayesian Paradigm -- Exercises -- 2 Markov Chain Monte Carlo Sampling -- 2.1 Gibbs Sampler -- 2.2 Metropolis-Hastings Algorithm -- 2.3 Hit-and-Run Algorithm -- 2.4 Multiple-Try Metropolis Algorithm -- 2.5 Grouping, Collapsing, and Reparameterizations -- 2.6 Acceleration Algorithms for MCMC Sampling -- 2.7 Dynamic Weighting Algorithm -- 2.8 Toward “Black-Box” Sampling -- 2.9 Convergence Diagnostics -- Exercises -- 3 Basic Monte Carlo Methods for Estimating Posterior Quantities -- 3.1 Posterior Quantities -- 3.2 Basic Monte Carlo Methods -- 3.3 Simulation Standard Error Estimation -- 3.4 Improving Monte Carlo Estimates -- 3.5 Controlling Simulation Errors -- Exercises -- 4 Estimating Marginal Posterior Densities -- 4.1 Marginal Posterior Densities -- 4.2 Kernel Methods -- 4.3 IWMDE Methods -- 4.4 Illustrative Examples -- 4.5 Performance Study Using the Kullback-Leibler Divergence -- Exercises -- 5 Estimating Ratios of Normalizing Constants -- 5.1 Introduction -- 5.2 Importance Sampling -- 5.3 Bridge Sampling -- 5.4 Path Sampling -- 5.5 Ratio Importance Sampling -- 5.6 A Theoretical Illustration -- 5.7 Computing Simulation Standard Errors -- 5.8 Extensions to Densities with Different Dimensions -- 5.9 Estimation of Normalizing Constants After Transformation -- 5.10 Other Methods -- 5.11 An Application of Weighted Monte Carlo Estimators -- 5.12 Discussion -- Exercises -- 6 Monte Carlo Methods for Constrained Parameter Problems -- 6.1 Constrained Parameter Problems -- 6.2 Posterior Moments and Marginal Posterior Densities -- 6.3 Computing Normalizing Constants for Bayesian Estimation -- 6.4 Applications -- 6.5 Discussion -- Exercises -- 7 Computing Bayesian Credible and HPD Intervals -- 7.1 Bayesian Credible and HPD Intervals -- 7.2 Estimating Bayesian Credible Intervals -- 7.3 Estimating Bayesian HPD Intervals -- 7.4 Extension to the Constrained Parameter Problems -- 7.5 Numerical Illustration -- 7.6 Discussion -- Exercises -- 8 Bayesian Approaches for Comparing Nonnested Models -- 8.1 Marginal Likelihood Approaches -- 8.2 Scale Mixtures of Multivariate Normal Link Models -- 8.3 “Super-Model” or “Sub-Model” Approaches -- 8.4 Criterion-Based Methods -- 9 Bayesian Variable Selection -- 9.1 Variable Selection for Logistic Regression Models -- 9.2 Variable Selection for Time Series Count Data Models -- 9.3 Stochastic Search Variable Selection -- 9.4 Bayesian Model Averaging -- 9.5 Reversible Jump MCMC Algorithm for Variable Selection -- Exercises -- 10 Other Topics -- 10.1 Bayesian Model Adequacy -- 10.2 Computing Posterior Modes -- 10.3 Bayesian Computation for Proportional Hazards Models -- 10.4 Posterior Sampling for Mixture of Dirichlet Process Models -- Exercises -- References -- Author Index
Dimensions
unknown
Edition
1st ed. 2000.
Extent
1 online resource (XIII, 387 p.)
File format
multiple file formats
Form of item
online
Isbn
9781461212768
Level of compression
uncompressed
Media category
computer
Media type code
c
Other control number
10.1007/978-1-4612-1276-8
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000089470
  • (SSID)ssj0001297707
  • (PQKBManifestationID)11739659
  • (PQKBTitleCode)TC0001297707
  • (PQKBWorkID)11229465
  • (PQKB)11209538
  • (DE-He213)978-1-4612-1276-8
  • (MiAaPQ)EBC3075160
  • (EXLCZ)993400000000089470
Label
Monte Carlo Methods in Bayesian Computation, by Ming-Hui Chen, Qi-Man Shao, Joseph G. Ibrahim, (electronic resource)
Publication
Note
"With 32 illustrations."
Antecedent source
mixed
Bibliography note
Includes bibliographical references and indexes
Carrier category
online resource
Carrier category code
cr
Color
not applicable
Content category
text
Content type code
txt
Contents
1 Introduction -- 1.1 Aims -- 1.2 Outline -- 1.3 Motivating Examples -- 1.4 The Bayesian Paradigm -- Exercises -- 2 Markov Chain Monte Carlo Sampling -- 2.1 Gibbs Sampler -- 2.2 Metropolis-Hastings Algorithm -- 2.3 Hit-and-Run Algorithm -- 2.4 Multiple-Try Metropolis Algorithm -- 2.5 Grouping, Collapsing, and Reparameterizations -- 2.6 Acceleration Algorithms for MCMC Sampling -- 2.7 Dynamic Weighting Algorithm -- 2.8 Toward “Black-Box” Sampling -- 2.9 Convergence Diagnostics -- Exercises -- 3 Basic Monte Carlo Methods for Estimating Posterior Quantities -- 3.1 Posterior Quantities -- 3.2 Basic Monte Carlo Methods -- 3.3 Simulation Standard Error Estimation -- 3.4 Improving Monte Carlo Estimates -- 3.5 Controlling Simulation Errors -- Exercises -- 4 Estimating Marginal Posterior Densities -- 4.1 Marginal Posterior Densities -- 4.2 Kernel Methods -- 4.3 IWMDE Methods -- 4.4 Illustrative Examples -- 4.5 Performance Study Using the Kullback-Leibler Divergence -- Exercises -- 5 Estimating Ratios of Normalizing Constants -- 5.1 Introduction -- 5.2 Importance Sampling -- 5.3 Bridge Sampling -- 5.4 Path Sampling -- 5.5 Ratio Importance Sampling -- 5.6 A Theoretical Illustration -- 5.7 Computing Simulation Standard Errors -- 5.8 Extensions to Densities with Different Dimensions -- 5.9 Estimation of Normalizing Constants After Transformation -- 5.10 Other Methods -- 5.11 An Application of Weighted Monte Carlo Estimators -- 5.12 Discussion -- Exercises -- 6 Monte Carlo Methods for Constrained Parameter Problems -- 6.1 Constrained Parameter Problems -- 6.2 Posterior Moments and Marginal Posterior Densities -- 6.3 Computing Normalizing Constants for Bayesian Estimation -- 6.4 Applications -- 6.5 Discussion -- Exercises -- 7 Computing Bayesian Credible and HPD Intervals -- 7.1 Bayesian Credible and HPD Intervals -- 7.2 Estimating Bayesian Credible Intervals -- 7.3 Estimating Bayesian HPD Intervals -- 7.4 Extension to the Constrained Parameter Problems -- 7.5 Numerical Illustration -- 7.6 Discussion -- Exercises -- 8 Bayesian Approaches for Comparing Nonnested Models -- 8.1 Marginal Likelihood Approaches -- 8.2 Scale Mixtures of Multivariate Normal Link Models -- 8.3 “Super-Model” or “Sub-Model” Approaches -- 8.4 Criterion-Based Methods -- 9 Bayesian Variable Selection -- 9.1 Variable Selection for Logistic Regression Models -- 9.2 Variable Selection for Time Series Count Data Models -- 9.3 Stochastic Search Variable Selection -- 9.4 Bayesian Model Averaging -- 9.5 Reversible Jump MCMC Algorithm for Variable Selection -- Exercises -- 10 Other Topics -- 10.1 Bayesian Model Adequacy -- 10.2 Computing Posterior Modes -- 10.3 Bayesian Computation for Proportional Hazards Models -- 10.4 Posterior Sampling for Mixture of Dirichlet Process Models -- Exercises -- References -- Author Index
Dimensions
unknown
Edition
1st ed. 2000.
Extent
1 online resource (XIII, 387 p.)
File format
multiple file formats
Form of item
online
Isbn
9781461212768
Level of compression
uncompressed
Media category
computer
Media type code
c
Other control number
10.1007/978-1-4612-1276-8
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000089470
  • (SSID)ssj0001297707
  • (PQKBManifestationID)11739659
  • (PQKBTitleCode)TC0001297707
  • (PQKBWorkID)11229465
  • (PQKB)11209538
  • (DE-He213)978-1-4612-1276-8
  • (MiAaPQ)EBC3075160
  • (EXLCZ)993400000000089470

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