Celebratio Mathematica

D. Blackwell: “Comparison of experiments,” pp. 93–102 in Proceedings of the second Berkeley symposium on mathematical statistics and probability (Berkeley, CA, 31 July–12 August 1950). Edited by J. Neyman. University of California Press (Berkeley and Los Angeles), 1951. MR 0046002 Zbl 0044.14203 inproceedings

Bohnenblust, Shapley, and Sherman [unpublished] have introduced a method of comparing two sampling procedures or experiments; essentially their concept is that one experiment \( \alpha \) is more informative than a second experiment \( \beta \), \( \alpha\supset\beta \), if, for every possible risk function, any risk attainable with \( \beta \) is also attainable with \( \alpha \). If \( \alpha \) is a sufficient statistic for a procedure equivalent to \( \beta \), \( \alpha\succ\beta \), it is shown that \( \alpha\supset\beta \). In the case of dichotomies, the converse is proved. Whether \( \succ \) and \( \supset \) are equivalent in general is not known. Various properties of \( \succ \) and \( \supset \) are obtained, such as the following: if \( \alpha\succ\beta \) and \( \gamma \) is independent of both, then the combination \( (\alpha,\gamma)\succ(\beta,\gamma) \). An application to a problem in \( 2{\times}2 \) tables is discussed.

D. Blackwell: “On a class of probability spaces,” pp. 1–6 in Proceedings of the third Berkeley symposium on mathematical statistics and probability (Berkeley, CA, 26–31 December 1954 and July–August 1955), vol. II. Edited by J. Neyman. University of California Press (Berkeley and Los Angeles), 1956. MR 0084882 Zbl 0073.12301 inproceedings

D. Blackwell: “Exponential error bounds for finite state channels,” pp. 57–63 in Proceedings of the fourth Berkeley symposium on mathematical statistics and probability (Berkeley, CA, 20 June–30 July 1960), vol. I. Edited by J. Neyman. University of California Press (Berkeley and Los Angeles), 1961. MR 0135199 Zbl 0104.11603 incollection

D. Blackwell: “Positive dynamic programming,” pp. 415–418 in Proceedings of the fifth Berkeley symposium on mathematical statististics and probability (Berkeley, CA, 21 June–18 July 1965), vol. I: Theory of statistics. Edited by L. M. Le Cam and J. Neyman. University of California Press (Berkeley and Los Angeles), 1967. MR 0218104 Zbl 0189.19804 incollection

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David H. Blackwell

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