Bernoulli 1713 Bayes 1763 Laplace 1813 : Anniversary Volume

The present volume represents the Proceedings of an International Research Seminar organized in 1963 by the Statistical Laboratory, Uni­ versity of California, Berkeley, on the occasion of a remarkable triple anniversary: the 250th anniversary of JACOB BERNOULLI'S "Ars Cony'ectandi", the 200th anniversary of THOMAS BAYES' "Essay towards solving a problem in doctrine of chance", and the 150th anniversary of the PIERRE-SnlO:-l" DE LAPLACE'S "Essai philosophique sur les probabilites". Financial assistance of the National Science Foundation, without which the Seminar could not have been held, is gratefully acknowledged. The pUblication of Ars Cony'ectandi, in 1713, was a milestone in the history of probability theory. Here, for the first time, appeared a careful description of the now well-known combinatorial methods which give solutions of many problems on simple games of chance. Also, Ars Conjectandi contains the Bernoulli numbers, theorems relating to the duration of games, and to the ruin of gamblers and, above all, the state­ ment and proof of the famous Bernoulli weak law of large numbers. Even though the original Latin edition of Ars Conjectandi was followed by several in modern languages, currently the book is not easily accessible. Apparently the last re-publication, in German, occurred in 1899, in two issues, No. 107 and No. 108, of the series "Ostwald's Klassi­ ker der exakten Wissenschaften", Wilhelm Engelman, Leipzig. The two books are difficult to locate Front Matter....Pages I-XII Contribution to the Theory of Epidemics....Pages 1-8 Study of Some Statistical Models Introduced by Problems of Physics....Pages 9-16 Stationary and Isotropic Random Functions....Pages 17-23 On the Estimation of a Multivariate Location Parameter with Squared Error Loss....Pages 24-29 Some Notes on Laplace....Pages 30-44 Extension of the Kolmogorov-Smirnov Test to Regression Alternatives....Pages 45-60 First-Passage Percolation, Subadditive Processes, Stochastic Networks, and Generalized Renewal Theory....Pages 61-110 Direct Product Branching Processes and Related Induced Markoff Chains I. Calculations of Rates of Approach to Homozygosity....Pages 111-145 Automatically Controlled Sequence of Statistical Procedures....Pages 146-178 On the Distribution of Sums of Independent Random Variables....Pages 179-202 Limit Solutions of Sequences of Statistical Games....Pages 203-208 Some Remarks on Statistical Inference....Pages 209-216 Approximation of Improper Prior Measures by Prior Probability Measures....Pages 217-240 Stationary Gaussian Processes Satisfying the Strong Mixing Condition and Best Predictable Functionals....Pages 241-252 Strong Limit Theorems for Stochastic Processes and Orthogonality Conditions for Probability Measures....Pages 253-262