E-Book, Englisch, 344 Seiten
Tan / Tian / Ng Bayesian Missing Data Problems
Erscheinungsjahr 2010
ISBN: 978-1-4200-7750-6
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
EM, Data Augmentation and Noniterative Computation
E-Book, Englisch, 344 Seiten
Reihe: Chapman & Hall/CRC Biostatistics Series
ISBN: 978-1-4200-7750-6
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
Bayesian Missing Data Problems: EM, Data Augmentation and Noniterative Computation presents solutions to missing data problems through explicit or noniterative sampling calculation of Bayesian posteriors. The methods are based on the inverse Bayes formulae discovered by one of the author in 1995. Applying the Bayesian approach to important real-world problems, the authors focus on exact numerical solutions, a conditional sampling approach via data augmentation, and a noniterative sampling approach via EM-type algorithms.
After introducing the missing data problems, Bayesian approach, and posterior computation, the book succinctly describes EM-type algorithms, Monte Carlo simulation, numerical techniques, and optimization methods. It then gives exact posterior solutions for problems, such as nonresponses in surveys and cross-over trials with missing values. It also provides noniterative posterior sampling solutions for problems, such as contingency tables with supplemental margins, aggregated responses in surveys, zero-inflated Poisson, capture-recapture models, mixed effects models, right-censored regression model, and constrained parameter models. The text concludes with a discussion on compatibility, a fundamental issue in Bayesian inference.
This book offers a unified treatment of an array of statistical problems that involve missing data and constrained parameters. It shows how Bayesian procedures can be useful in solving these problems.
Zielgruppe
Graduate students and researchers in statistics and biostatistics.
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
Introduction
Background
Scope, Aim and Outline
Inverse Bayes Formulae (IBF)
The Bayesian Methodology
The Missing Data Problems
Entropy
Optimization, Monte Carlo Simulation and Numerical Integration
Optimization
Monte Carlo Simulation
Numerical Integration
Exact Solutions
Sample Surveys with Nonresponse
Misclassified Multinomial Model
Genetic Linkage Model
Weibull Process with Missing Data
Prediction Problem with Missing Data
Binormal Model with Missing Data
The 2 × 2 Crossover Trial with Missing Data
Hierarchical Models
Nonproduct Measurable Space (NPMS)
Discrete Missing Data Problems
The Exact IBF Sampling
Genetic Linkage Model
Contingency Tables with One Supplemental Margin
Contingency Tables with Two Supplemental Margins
The Hidden Sensitivity Model for Surveys with Two Sensitive Questions
Zero-Inflated Poisson Model
Changepoint Problems
Capture-Recapture Model
Computing Posteriors in the EM-Type Structures
The IBF Method
Incomplete Pro-Post Test Problems
Right Censored Regression Model
Linear Mixed Models for Longitudinal Data
Probit Regression Models for Independent Binary Data
A Probit-Normal GLMM for Repeated Binary Data
Hierarchical Models for Correlated Binary Data
Hybrid Algorithms: Combining the IBF Sampler with the Gibbs Sampler
Assessing Convergence ofMCMC Methods
Remarks
Constrained Parameter Problems
Linear Inequality Constraints
Constrained Normal Models
Constrained Poisson Models
Constrained Binomial Models
Checking Compatibility and Uniqueness
Introduction
Two Continuous Conditional Distributions: Product Measurable Space (PMS)
Finite Discrete Conditional Distributions: PMS
Two Conditional Distributions: NPMS
One Marginal and Another Conditional Distribution
Appendix: Basic Statistical Distributions and Stochastic Processes
Discrete Distributions
Continuous Distributions
Mixture Distributions
Stochastic Processes
References
Author Index
Subject Index
Problems appear at the end of each chapter.
