# 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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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.

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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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