Introduction to Probability Simulation and Gibbs Sampling with R

A practical introduction to Monte Carlo simulation that provides background in other topics, this book explains the rationale for and the use of the Gibbs Sampler as a simulation tool used in applied probability and statistics.

Simulation has become a basic tool for the practice of applied probability and statistics. This is the first presentation of the Gibbs Sampler at an elementary level. The audience will be beginning graduate students in statistics and operations research.

Probability simulation using R inlcuding the simulations of the Law of Large numbers and the Central Limit Theorem Introduces the most common methods of Monte Carlo integration using R. Gibbs sampling introduced using R and WinBUGS to obtain interval estimates; graphical diagnostic methods used to illustrate speed of convergence.

Autorentext
Eric A. Suess is Chair and Professor of Statistics and Biostatistics and Bruce E. Trumbo is Professor Emeritus of Statistics and Mathematics, both at California State University, East Bay. Professor Suess is experienced in applications of Bayesian methods and Gibbs sampling to epidemiology. Professor Trumbo is a fellow of the American Statistical Association and the Institute of Mathematical Statistics, and he is a recipient of the ASA Founders Award and the IMS Carver Medallion.

Inhalt
Introductory Examples: Simulation, Estimation, and Graphics.- Generating Random Numbers.- Monte Carlo Integration and Limit Theorems.- Sampling from Applied Probability Models.- Screening Tests.- Markov Chains with Two States.- Examples of Markov Chains with Larger State Spaces.- to Bayesian Estimation.- Using Gibbs Samplers to Compute Bayesian Posterior Distributions.- Using WinBUGS for Bayesian Estimation.- Appendix: Getting Started with R.