Introduction to probability and statistics from a Bayesian viewpoint, - Inference part 2

The two parts of this book treat probability and statistics as mathematical disciplines and with the same degree of rigour as is adopted for other branches of applied mathematics at the level of a British honours degree. They contain the minimum information about these subjects that any honours graduate in mathematics ought to know. They are written primarily for general mathematicians, rather than for statistical specialists or for natural scientists who need to use statistics in their work. No previous knowledge of probability or statistics is assumed, though familiarity with calculus and linear algebra is required. The first volume takes the theory of probability sufficiently far to be able to discuss the simpler random processes, for example, queueing theory and random walks. The second volume deals with statistics, the theory of making valid inferences from experimental data, and includes an account of the methods of least squares and maximum likelihood; it uses the results of the first volume. CONTENTS......Page 7 Preface......Page 9 5.1 Bayes's theorem and the normal distribution......Page 15 5.2 Vague prior knowledge and interval estimates for the normal mean......Page 27 5.3 Interval estimates for the normal variance......Page 40 5.4 Interval estimates for the normal mean and variance......Page 50 5.5 Sufficiency......Page 60 5.6 Significance tests and the likelihood principle......Page 72 Exercises......Page 85 6.1 Comparison of two means......Page 90 6.2 Comparison of two variances......Page 100 6.3 General comparison of two means......Page 105 6.4 Comparison of several means......Page 109 6.5 Analysis of variance: between and within samples......Page 118 6.6 Combination of observations......Page 126 Exercises......Page 136 7.1 The method of maximum likelihood......Page 142 7.2 Random sequences of trials......Page 155 7.3 The Poisson distribution......Page 167 7.4 Goodness-of-fit tests......Page 171 7.5 Goodness-of-fit tests (continued) page......Page 182 7.6 Contingency tables......Page 190 Exercises......Page 199 8.1 Linear homoscedastic normal regression......Page 217 8.2 Correlation coefficient......Page 228 8.3 Linear hypothesis......Page 235 8.4 Computational methods......Page 250 8.5 Two-way classification......Page 260 8.6 Further applications of linear hypothesis theo ry......Page 271 Exercises......Page 284 Appendix. Two-sided tests for the X2-distribution......Page 296 Bibliography......Page 299 Subject Index......Page 301 Index of Notations......Page 306