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Article Contents

TITLE PAGE

ORIGINAL PREFACE

PREFACE TO REVISED EDITION

1.DIRECT PROBABILITY

2.INVERSE PROBABILITY

3.LIKELIHOOD RATIOS

4.MAXIMUM-LIKELIHOOD METHOD

5.GAUSSIAN DISTRIBUTIONS

6.MAXIMUM-LIKELIHOOD ERROR, ONE PARAMETER

7.MAXIMUM-LIKELIHOOD ERRORS, M-PARAMETERS CORRELATED ERRORS

8.PROPAGATION OF ERRORS: THE ERROR MATRIX

9.SYSTEMATIC ERRORS

10.UNIQUENESS OF MAXIMUM-LIKELIHOOD SOLUTION

11.CONFIDENCE INTERVALS AND THEIR ARBITRARINESS

12.BINOMIAL DISTRIBUTION

13.POISSON DISTRIBUTION

14.GENERALIZED MAXIMUM-LIKELIHOOD METHOD

15.THE LEAST-SQUARES METHOD

16.GOODNESS OF FIT, THE chi2 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