The Estimation Of Probabilities An Essay on Modern Bayesian Methods

by Good, Irving John

• ISBN13: 9780262570152
• ISBN10: 0262570157
• Format: Paperback
• Copyright: 2003-03-17
• Publisher: The MIT Press

Summary

The problem of how to estimate probabilities has interested philosophers, statisticians, actuaries, and mathematicians for a long time. It is currently of interest for automatic recognition, medical diagnosis, and artificial intelligence in general. The main purpose of this monograph is to review existing methods, especially those that are new or have not been written up in a connected manner. The need for nontrivial theory arises because our samples are usually too small for us to rely exclusively on the frequency definition of probability. Most of the techniques described in this book depend on a modern Bayesian approach. The maximum-entropy principle, also relevant to this discussion, is used in the last chapter. It is hoped that the book will stimulate further work in a field whose importance will increasingly be recognized. Methods for estimating probabilities are related to another part of statistics, namely, significance testing, and examples of this relationship are also presented. Many readers will be persuaded by this work that it is necessary to make use of a theory of subjective probability in order to estimate physical probabilities; and also that a useful idea is that of a hierarchy of three types of probability which can sometimes be identified with, physical, logical, and subjective probabilities. The Estimation of Probabilitiesis intended for statisticians, probabilists, philosophers of science, mathematicians, medical diagnosticians, and workers on artificial intelligence.

Author Biography

Irving Good was University Distinguished Professor of Statistics at Virginia Polytechnic Institute and State University as well as an adjunct professor of the Center for the Study of Science in Society and an adjunct professor of Philosophy.

Table of Contents

Foreword	p. vii
Preface	p. ix
Introduction	p. 3
Kinds of Probability	p. 6
Simple Sampling	p. 12
Multiple Sampling	p. 21
Multinomial Discrimination and Significance	p. 31
Tests for Independence in Contingency Tables	p. 49
Large Pure Contingency Tables	p. 57
The Sampling of Species	p. 67
Multidimensional Population Contingency Tables	p. 72
Summary	p. 77
The Incompatibility of Fiducial and Bayesian Inference	p. 81
Hausdorff Summation as a Monte Carlo Process	p. 84
Folded Contingency Tables	p. 85
A Minimax Property of Singular Values of a Matrix	p. 87
Learning from Experience in the Treatment of Contingency Tables	p. 90
References	p. 97
Index	p. 103
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