For a postscript version of the article, click here.

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.