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JN-25 was the primary World War II Japanese naval cipher. It was introduced in 1939 and evolved throughout the war, presenting US Navy codebreakers with a succession of challenges. When JN-25N-62 was introduced on 25 July 1944, one question that arose for US Navy codebreakers was the function of two digits in the starting point indicator: did they represent a pair of single-digit numbers or a single two-digit number? US Navy codebreakers knew Japanese cipher clerks often chose an additive in the leftmost column of a page of additives as the starting point for the string of text additives. This lack of randomness enabled an attack on the indicator. Navy codebreakers used a statistical test to decide between the two possibilities. Construction of the necessary probability tables was assigned to Temple Rice Hollcroft, a mathematician on the faculty of Wells College. Hollcroft's problem is documented in an internal Navy history, but that history raises almost as many questions as it answers. This article explores the construction of Hollcroft's tables, how they were used, and why Hollcroft was selected to construct the tables. [ABSTRACT FROM AUTHOR]

By now, a great deal is known about the contributions of Alan Turing, I. J. Good, Max Newman, and other mathematicians who worked at Bletchley Park during World War II. But what about the other side? Until recently, very little was known about the German mathematicians who aided the Nazi war effort: who were they, where did they work, and what did they do? But now, thanks to the release of a large number of TICOM documents in recent years, an initial picture is beginning to emerge. In this article, we identify the most important mathematicians who worked in the different German cryptologic organizations during the war: who they were, how they were recruited, which organizations they were in, and what they did (when this is known). Although their successes never rivaled those of Bletchley Park, they did have successes, and these were sometimes due to the efforts of mathematicians who went on to have distinguished careers after the war. One question that motivated this study was to understand the reasons for the German communications security meltdown during the war: how they got the Enigma and Tunny security assessments partly right but mostly wrong. As will be seen, this was not due to a lack of talent: some of the very best German mathematicians contributed to their war effort. The answer lies instead in how these potentially very useful assets were actually used (in striking contrast with what happened at Bletchley Park). [ABSTRACT FROM AUTHOR]

In addition to his contributions to biostatistics and clinical trials, Paul Meier had a long-term interest in the legal applications of statistics. As part of this, he had extensive experience as a statistical consultant. Legal consulting can be a minefield, but as a result of his background, Paul had excellent advice to give to those starting out on how to function successfully in this environment. [ABSTRACT FROM AUTHOR]

In April 2012, two papers written by Alan Turing during the Second World War on the use of probability in cryptanalysis were released by GCHQ. The longer of these presented an overall framework for the use of Bayes's theorem and prior probabilities, including four examples worked out in detail: the Vigenère cipher, a letter subtractor cipher, the use of repeats to find depths, and simple columnar transposition. (The other paper was an alternative version of the section on repeats.) Turing stressed the importance in practical cryptanalysis of sometimes using only part of the evidence or making simplifying assumptions and presents in each case computational shortcuts to make burdensome calculations manageable. The four examples increase roughly in their difficulty and cryptanalytic demands. After the war, Turing's approach to statistical inference was championed by his assistant in Hut 8, Jack Good, which played a role in the later resurgence of Bayesian statistics. [ABSTRACT FROM PUBLISHER]

Jeffrey's rule for revising a probability P to a new probability P* based on new probabilities P* (E[sub I]) on a partition {E[sub I]}[sub I = 1[sup n]] is P[sup *](A) = SIGMA P(A | E[sub I])P[sup *](E[sub I]). Jeffrey's rule is applicable if it is judged that P[sup *](A | E[sub I]) = P(A | E[sub I]) for all A and I. This article discusses some of the mathematical properties of this rule, connecting it with sufficient partitions, and maximum entropy updating of contingency tables. The main results concern simultaneous revision on two partitions. [ABSTRACT FROM AUTHOR]

The Howland will case is possibly the earliest instance in American law of the use of probabilistic and statistical evidence. Identifying 30 downstrokes in the signature of Sylvia Ann Howland, Benjamin Peirce attempted to show that a contested signature on a will had been traced from another and genuine signature. He argued that their agreement in all 30 downstrokes was improbable in the extreme under a binomial model. Peirce supported his model by providing a graphical test of goodness of fit. We give a critique of Peirce's model and discuss the use and abuse of the "product rule" for multiplying probabilities of independent events. [ABSTRACT FROM AUTHOR]