Introduction to Probability Simulation and Gibbs Sampling with R
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. Application
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Eric A. Suess • Bruce E. Trumbo
Introduction to Probability Simulation and Gibbs Sampling with R
Eric A. Suess Department of Statistics and Biostatistics California State University, East Bay Hayward, CA 94542-3087 USA [email protected]
Bruce E. Trumbo Department of Statistics and Biostatistics California State University, East Bay Hayward, CA 94542-3087 USA [email protected]
ISBN 978-0-387-40273-4 e-ISBN 978-0-387-68765-0 DOI 10.1007/978-0-387-68765-0 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2010928331 © Springer Science+Business Media, LLC 2010 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
We dedicate this book to our students.
Preface
Our primary motivation in writing this book is to provide a basic introduction to Gibbs sampling. However, the early chapters are written so that the book can also serve as an introduction to simulating probability models or to computational aspects of Markov chains. Prerequisites are a basic course in statistical inference (including data description, and confidence intervals using t and chi-squared distributions) and a post-calculus course in probability theory (including binomial, Poisson, normal, gamma, and beta families of distributions, conditional and joint distributions, and the Law of Large Numbers). Accordingly, the target audience is upper-division BS or first-year MS students and practitioners of statistics with a knowledge of these prerequisites. Specific Topics. Many students at the target level lack the full spectrum of experience necessary to understand Gibbs sampling, and thus much of the book is devoted to laying an appropriate foundation. Here are some specifics. The first four chapters introduce the ideas of random number generation and probability simulation. Fruitful use of simulation requires the right mixture of confidence that it can often work quite well, consideration of margins of error, and skepticism about whether necessary assumptions are met. Most of our early examples of simulation contain a component for which exact analytical results are available as a reality check. Some theoretical justifications based on the Law of Large Numb
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