By R. Bartoszyński, J. Łoś, M. Wycech-Łoś (auth.), Jerzy Neyman, Lucien M. Le Cam (eds.)
Read or Download Bernoulli 1713 Bayes 1763 Laplace 1813: Anniversary Volume Proceedings of an International Research Seminar Statistical Laboratory University of California, Berkeley 1963 PDF
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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
It would be no help if one could project oneself backwards through time and actually ask the person concerned. What we think depends not only on our genetical makeup, but also on the outside influences at work at the particular point in the space-time continuum at which we find ourselves. Thus when, centuries from now, someone rises to commemorate the discoverer of confidence intervals, it would be stimulating to have on record why he pursued that particular problem at that particular time-stimulating but no more, because he is as much a prisoner of his time and circumstance as LAPLACE was of his.
Let us consider two extreme cases. R x, Fig. 3. Volume considerably larger than the "correlation distance a" Fig. 4. Cylinder alined along the direction of the propag ation 1. The volume nf/' is, in all directions, considerably larger than the "correlation distance a" (Fig. 3). Then, it is easy to prove that E (\P'1 (~) \2 )= 4r;:k3s,_. F. 11 (M) = 11 (x1 , x 2 , x 3). Then, by studying experimentally the scattering at a larg~ distance, we can obtain the three-dimensional spectral density s,.. (K), under the obvious condition that K may be taken experimentally in a sufficiently large range.
21) p Case 2. n f/1 But f/ 1 [t/J (e)] = [rf> (e)] = Am [tp (u1)] tfJ (u1)u,=p; hence . 23) solve our problem for an arbitrary value of n. Let us now consider some particular cases. Particular cases. a) n = 2. 24) - This formula was used by B. PICINBONO  and M. SAVELL!  and applied to the study of the granularity of photographic films. b) n = 3. 25) Remarks. 1. ([)(e) is surely nonnegative. 25), q; (u 1 ) is certainly a nonincreasing function of I u 1 I· This result is strongly connected with the fact that n = 3.