Bernoulli 1713, Bayes 1763, Laplace 1813: Anniversary Volume. Proceedings of an International Research Seminar Statistical Laboratory University of Ca

ISBN-13: 9783642494666 / Niemiecki / Miękka / 1965 / 262 str.

Jerzy Neyman; Lucienglish M. Le Cam

Opis

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 Conjectandi," the 200th anniversary of THOMAS BAYES' "Essay towards solving a problem in doctrine of chance," and the 150th anniversary of the PIERRE-SIMON 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 Conjectandi, 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.

Spis treści

Contribution to the theory of epidemics.- Study of some statistical models introduced by problems of physics.- Stationary and isotropic random functions.- On the estimation of a multivariate location parameter with squared error loss.- Some notes on Laplace.- Extension of the Kolmogorov-Smirnov test to regression alternatives.- First-passage percolation, subadditive processes, stochastic networks, and generalized renewal theory.- Direct product branching processes and related induced Markoff chains. I. Calculations of rates of approach to homozygosity.- Automatically controlled sequence of statistical procedures.- On the distribution of sums of independent random variables.- Limit solutions of sequences of statistical games.- Some remarks on statistical inference.- Approximation of improper prior measures by prior probability measures.- Stationary Gaussian processes satisfying the strong mixing condition and best predictable functionals.- Strong limit theorems for stochastic processes and orthogonality conditions for probability measures.