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Introduction to Bayesian statistics - Bolstad M.

Introduction to Bayesian statistics

Author: Bolstad M.
Publishers: Wiley Publishing
Year of publication: 2004
Number of pages: 361
ISBN 0-471-27020-2
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Download: introductiontobayesianstatistics2004.pdf

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Introduction to Bayesian Statistics
William M. Bolstad
University of Waikato Hamilton, New Zealand
WILEY-INTERSCIENCE
A JOHN WILEY & SONS, INC., PUBLICATION
Copyright © 2004 by John Wiley & Sons, Inc. All rights reserved.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey.
Published simultaneously in Canada.
No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 646-8600, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., Ill River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008.
Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.
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Library of Congress Cataloging-in-Publication Data:
Bolstad, William М., 1943-
Introduction to Bayesian statistics / William M. Bolstad. p. cm.
Includes bibliographic references and index.
ISBN 0-471-27020-2 (cloth)
1. Bayesian statistical decision theory. I. Title.
QA279.5.B65 2004
519.5'42—dc22 2003057660
Printed in the United States of America.
10 987654321
This book is dedicated to
Sylvie, Ben, Rachel, Mary, and Elizabeth
Contents
Preface xiii
1 Introduction to Statistical Science 1
1.1 The Scientific Method: A Process for Learning 3
1.2 The Role of Statistics in the Scientific Method 4
1.3 Main Approaches to Statistics 5
1.4 Purpose and Organization of This Text 8
2 Scientific Data Gathering 13
2.1 Sampling from a Real Population 14
2.2 Observational Studies and Designed Experiments 17
Monte Carlo Exercises 22
3 Displaying and Summarizing Data 29
3.1 Graphically Displaying a Single Variable 29
3.2 Graphically Comparing Two Samples 37
3.3 Measures of Location 39
vii
viii CONTENTS
3.4 Measures of Spread 42
3.5 Displaying Relationships Between Two or More
Variables 44
3.6 Measures of Association for Two or More Variables 46
Exercises 50
4 Logic, Probability, and Uncertainty 55
4.1 Deductive Logic and Plausible Reasoning 56
4.2 Probability 58
4.3 Axioms of Probability 59
4.4 Joint Probability and Independent Events 60
4.5 Conditional Probability 62
4.6 Bayes ’ Theorem 63
4.7 Assigning Probabilities 68
4.8 Odds Ratios and Bayes Factor 69
Exercises 73
5 Discrete Random Variables 75
5.1 Discrete Random Variables 76
5.2 Probability Distribution of a Discrete Random
Variable 78
5.3 Binomial Distribution 81
5.4 Hypergeometric Distribution 83
5.5 Joint Random Variables 84
5.6 Conditional Probability for Joint Random Variables 88
Exercises 92
6 Bayesian Inference for Discrete Random Variables 95
6.1 Two Equivalent Ways of Using Bayes ’ Theorem 100
6.2 Bayes ’ Theorem for Binomial with Discrete Prior 102
6.3 Important Consequences of Bayes ’ Theorem 105
Exercises 106
Computer Exercises 108
CONTENTS ix
7 Continuous Random Variables 111
7.1 Probability Density Function 113
7.2 Some Continuous Distributions 116
7.3 Joint Continuous Random Variables 122
7.4 Joint Continuous and Discrete Random Variables 123
Exercises 126
8 Bayesian Inference for Binomial Proportion 129
8.1 Using a Uniform Prior 130
8.2 Using a Beta Prior 131
8.3 Choosing Your Prior 133
8.4 Summarizing the Posterior Distribution 136
8.5 Estimating the Proportion 139
8.6 Bayesian Credible Interval 140
Exercises 143
Computer Exercises 145
9 Comparing Bayesian and Frequentist Inferences for Proportion 14 7
9.1 Frequentist Interpretation of Probability and
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