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  • Textbook
  • © 2010

Introduction to Probability Simulation and Gibbs Sampling with R

  • 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.

Part of the book series: Use R! (USE R)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xiii
  2. Introductory Examples: Simulation, Estimation, and Graphics

    • Eric A. Suess, Bruce E. Trumbo
    Pages 1-22
  3. Generating Random Numbers

    • Eric A. Suess, Bruce E. Trumbo
    Pages 23-49
  4. Monte Carlo Integration and Limit Theorems

    • Eric A. Suess, Bruce E. Trumbo
    Pages 51-85
  5. Sampling from Applied Probability Models

    • Eric A. Suess, Bruce E. Trumbo
    Pages 87-117
  6. Screening Tests

    • Eric A. Suess, Bruce E. Trumbo
    Pages 119-138
  7. Markov Chains with Two States

    • Eric A. Suess, Bruce E. Trumbo
    Pages 139-158
  8. Examples of Markov Chains with Larger State Spaces

    • Eric A. Suess, Bruce E. Trumbo
    Pages 159-193
  9. Introduction to Bayesian Estimation

    • Eric A. Suess, Bruce E. Trumbo
    Pages 195-218
  10. Using Gibbs Samplers to Compute Bayesian Posterior Distributions

    • Eric A. Suess, Bruce E. Trumbo
    Pages 219-248
  11. Using WinBUGS for Bayesian Estimation

    • Eric A. Suess, Bruce E. Trumbo
    Pages 249-274
  12. Appendix: Getting Started with R

    • Eric A. Suess, Bruce E. Trumbo
    Pages 275-299
  13. Back Matter

    Pages 301-307

About this book

The first seven chapters use R for probability simulation and computation, including random number generation, numerical and Monte Carlo integration, and finding limiting distributions of Markov Chains with both discrete and continuous states. Applications include coverage probabilities of binomial confidence intervals, estimation of disease prevalence from screening tests, parallel redundancy for improved reliability of systems, and various kinds of genetic modeling. These initial chapters can be used for a non-Bayesian course in the simulation of applied probability models and Markov Chains. Chapters 8 through 10 give a brief introduction to Bayesian estimation and illustrate the use of Gibbs samplers to find posterior distributions and interval estimates, including some examples in which traditional methods do not give satisfactory results. WinBUGS software is introduced with a detailed explanation of its interface and examples of its use for Gibbs sampling for Bayesian estimation.
No previous experience using R is required. An appendix introduces R, and complete R code is included for almost all computational examples and problems (along with comments and explanations). Noteworthy features of the book are its intuitive approach, presenting ideas with examples from biostatistics, reliability, and other fields; its large number of figures; and its extraordinarily large number of problems (about a third of the pages), ranging from simple drill to presentation of additional topics. Hints and answers are provided for many of the problems. These features make the book ideal for students of statistics at the senior undergraduate and at the beginning graduate levels.

Reviews

From the reviews:

“Suess and Trumbo’s book ‘Introduction to Probability Simulation and Gibbs Sampling with R,’ part of the ‘Use R!’ series, fits precisely into this framework of learning by doing—and doing again, with different distributions, or different parameters, or under different scenarios. … The book also contains an Appendix with an introduction to R, which should make it particularly attractive to students, who won’t have to go to another source to learn about the basics. … an overall very useful book.” (Nicole Lazar, Technometrics, Vol. 53 (3), August, 2011)

Authors and Affiliations

  • , Department of Statistics and Biostatisti, California State University, East Bay, Hayward, USA

    Eric A. Suess, Bruce E. Trumbo

About the authors

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.

Bibliographic Information

Buy it now

Buying options

eBook USD 79.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access