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Table of Contents

ORIGINAL PREFACE

PREFACE TO REVISED EDITION

DIRECT PROBABILITY

INVERSE PROBABILITY

LIKELIHOOD RATIOS

MAXIMUM-LIKELIHOOD METHOD

GAUSSIAN DISTRIBUTIONS

MAXIMUM-LIKELIHOOD ERROR, ONE PARAMETER

MAXIMUM-LIKELIHOOD ERRORS, M-PARAMETERS CORRELATED ERRORS

PROPAGATION OF ERRORS: THE ERROR MATRIX

SYSTEMATIC ERRORS

UNIQUENESS OF MAXIMUM-LIKELIHOOD SOLUTION

CONFIDENCE INTERVALS AND THEIR ARBITRARINESS

BINOMIAL DISTRIBUTION

POISSON DISTRIBUTION

GENERALIZED MAXIMUM-LIKELIHOOD METHOD

THE LEAST-SQUARES METHOD

GOODNESS OF FIT, THE ² DISTRIBUTION

APPENDIX I: PREDICTION OF LIKELIHOOD RATIOS

APPENDIX II: DISTRIBUTION OF THE LEAST-SQUARES SUM

APPENDIX III. LEAST SQUARES WITH ERRORS IN BOTH VARIABLES

APPENDIX IV. NUMERICAL METHODS FOR MAXIMUM LIKELIHOOD AND LEAST SQUARES SOLUTIONS

APPENDIX V. CUMULATIVE GAUSSIAN AND CGI-SQUARED DISTRIBUTIONS

REFERENCES

Erratum: The correct formula for the square root of the variance of a binomial distribution is (p) = [p(1 - p) / N]^1/2, where N is the number of trials and p is the probability of success.