William M. Bolstad

Understanding Computational Bayesian Statistics

• Gebundenes Buch

Produktbeschreibung

A hands-on introduction to computational statistics from a Bayesian point of view

Providing a solid grounding in statistics while uniquely covering the topics from a Bayesian perspective, Understanding Computational Bayesian Statistics successfully guides readers through this new, cutting-edge approach. With its hands-on treatment of the topic, the book shows how samples can be drawn from the posterior distribution when the formula giving its shape is all that is known, and how Bayesian inferences can be based on these samples from the posterior. These ideas are illustrated on common statistical models, including the multiple linear regression model, the hierarchical mean model, the logistic regression model, and the proportional hazards model.

The book begins with an outline of the similarities and differences between Bayesian and the likelihood approaches to statistics. Subsequent chapters present key techniques for using computer software to draw Monte Carlo samples from the incompletely known posterior distribution and performing the Bayesian inference calculated from these samples. Topics of coverage include:

Direct ways to draw a random sample from the posterior by reshaping a random sample drawn from an easily sampled starting distribution

The distributions from the one-dimensional exponential family

Markov chains and their long-run behavior

The Metropolis-Hastings algorithm

Gibbs sampling algorithm and methods for speeding up convergence

Markov chain Monte Carlo sampling

Using numerous graphs and diagrams, the author emphasizes a step-by-step approach to computational Bayesian statistics. At each step, important aspects of application are detailed, such as how to choose a prior for logistic regression model, the Poisson regression model, and the proportional hazards model. A related Web site houses R functions and Minitab(r) macros for Bayesian analysis and Monte Carlo simulations, and detailed appendices in the book guide readers through the use of these software packages.

Understanding Computational Bayesian Statistics is an excellent book for courses on computational statistics at the upper-level undergraduate and graduate levels. It is also a valuable reference for researchers and practitioners who use computer programs to conduct statistical analyses of data and solve problems in their everyday work.

Produktdetails

• Wiley Series in Computational Statistics
• Verlag: Wiley & Sons
• 1. Auflage
• Seitenzahl: 336
• Erscheinungstermin: 1. Dezember 2009
• Englisch
• Abmessung: 240mm x 161mm x 22mm
• Gewicht: 665g
• ISBN-13: 9780470046098
• ISBN-10: 0470046090
• Artikelnr.: 27139093

Autorenporträt

WILLIAM M. BOLSTAD, PHD, is Senior Lecturer in the Department of Statistics at The University of Waikato (New Zealand). Dr. Bolstad's research interests include Bayesian statistics, MCMC methods, recursive estimation techniques, multiprocess dynamic time series models, and forecasting. He is the author of Introduction to Bayesian Statistics, Second Edition, also published by Wiley.

Inhaltsangabe

Preface. 1 Introduction to Bayesian Statistics. 1.1 The Frequentist
Approach to Statistics. 1.2 The Bayesian Approach to Statistics. 1.3
Comparing Likelihood and Bayesian Approaches to Statistics. 1.4
Computational Bayesian Statistics. 1.5 Purpose and Organization of This
Book. 2 Monte Carlo Sampling from the posterior. 2.1
Acceptance-Rejection-Sampling. 2.2 Sampling-Importance-Resampling. 2.3
Adaptive-Rejection-Sampling from a Log-Concave Distribution. 2.4 Why Direct
Methods are Inefficient for High-Dimension Parameter Space. 3 Bayesian
Inference. 3.1 Bayesian Inference from the Numerical Posterior. 3.2
Bayesian Inference from Posterior Random Sample. 4 Bayesian Statistics
using Conjugate Priors. 4.1 One-Dimensional Exponential Family of
Densities. 4.2 Distributions for Count Data. 4.3 Distributions for Waiting
Times. 4.4 Normally Distributed Observations with Known Variance. 4.5
Normally Distributed Observations with Known Mean. 4.6 Normally Distributed
Observations with Unknown Mean and Variance. 4.7 Multivariate Normal
Observations with Known Covariance Matrix. 4.8 Observations from Normal
Linear Regression Model. Appendix: Proof of Poisson Process Theorem. 5
Markov Chains. 5.1 Stochastic Processes. 5.2 Markov Chains. 5.3
Time-Invariant Markov Chains with Finite State Space. 5.4 Classification of
States of a Markov Chain. 5.5 Sampling from a Markov Chain. 5.6
Time-Reversible Markov Chains and Detailed Balance. 5.7 Markov Chains with
Continuous State Space. 6 Markov Chain Monte Carlo Sampling from Posterior.
6.1 Metropolis-Hastings Algorithm for a Single Parameter. 6.2
Metropolis-Hastings Algorithm for Multiple Parameters. 6.3 Blockwise
Metropolis-Hastings Algorithm. 6.4 Gibbs Sampling . 6.5 Summary. 7
Statistical Inference from a Markov Chain Monte Carlo Sample. 7.1 Mixing
Properties of the Chain. 7.2 Finding a Heavy-Tailed Matched Curvature
Candidate Density. 7.3 Obtaining An Approximate Random Sample For
Inference. Appendix: Procedure for Finding the Matched Curvature Candidate
Density for a Multivariate Parameter. 8 Logistic Regression. 8.1 Logistic
Regression Model. 8.2 Computational Bayesian Approach to the Logistic
Regression Model. 8.3 Modelling with the Multiple Logistic Regression
Model. 9 Poisson Regression and Proportional Hazards Model. 9.1 Poisson
Regression Model. 9.2 Computational Approach to Poisson Regression Model.
9.3 The Proportional Hazards Model. 9.4 Computational Bayesian Approach to
Proportional Hazards Model. 10 Gibbs Sampling and Hierarchical Models. 10.1
Gibbs Sampling Procedure. 10.2 The Gibbs Sampler for the Normal
Distribution. 10.3 Hierarchical Models and Gibbs Sampling. 10.4 Modelling
Related Populations with Hierarchical Models. Appendix: Proof that Improper
Jeffrey's Prior Distribution for the Hypervariance Can Lead to an Improper
Posterior. 11 Going Forward with Markov Chain Monte Carlo. A Using the
Included Minitab Macros. B Using the Included R Functions. References.
Topic Index.