By R. Bartoszyński, J. Łoś, M. Wycech-Łoś (auth.), Jerzy Neyman, Lucien M. Le Cam (eds.)
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Extra info for Bernoulli 1713, Bayes 1763, Laplace 1813: Anniversary Volume. Proceedings of an International Research Seminar Statistical Laboratory University of California, Berkeley 1963
R (M) must give the two-dimensional spectral density q>2 (e). r on the xl-axis. But if we do this, we must then be able to compute q>2 (e) from CfJI (u l ). Scattering of a plane wave by a volume "Y of a stationary and isotropic random medium [4J, (Fig. 2). As an example, we consider an acoustical wave . -I'ot) . 4) 2* 20 A. BLANC-LAPIERRE and P. FAURE We consider the scattering at a large distance produced by a bounded volume "Y of a medium whose refractive index n (Xl> X2 , xa) = 1 + + fl (Xl' X 2, xa), with Ifll < < 1, is stationary and isotropic.
E. E. ~* is at most 0 (h) for small h. The other possibility is that EY = t; oF O. This situation can be reduced to the one treated within the model by replacing. Y by y* = Y -t; and ~ by ~* = ~ + t;. 2). E. E. ~ ~ e + 2 It; I VB + t;2 . 3. Application to Bayesian problems In this section ~ and Yare both random variables in r dimensional Euclidean space, X = Y +~, and the problem still is to estimate ~, based on the observation X, with squared error loss. We treat only the simplest of various hypotheses allowing the application of the previous section.
Math. Statist. 1 (1964). : Inadmissibility of the usual estimator for the mean of a multivariate normal distribution. Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability. 1. 197 (1956). Some Notes on Laplace* By F. N. DAVID University College, London and University of California, Berkeley I should begin, I suppose, by confessing that my talk of today was concocted under something of a misapprehension. When I heard that we were to commemorate JAMES BERNOULLI, THOMAS BAYES and PIERRESIMON DE LAPLACE, I envisaged an exercise similar to that carried out by my own college each year in memory of JEREMY BENTHAM, and I prepared myself accordingly.