Sandy L. Zabell

Updating Subjective Probability

Abstract Jeffreys rule for revising a probability P to a new probability P* based on new probabilities P* (Ei ) on a partition {Ei } i = 1 n is P*(A) = Σ P(A| Ei ) P* (Ei ). Jeffreys rule is applicable if it is judged that P* (A | Ei ) = P(A | Ei ) 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.

Ronald Aylmer Fisher

R. A. Fisher transformed the statistics of his day from a modest collection of useful ad hoc techniques into a powerful and systematic body of theoretical concepts and practical methods. This achievement was all the more impressive because at the same time he pursued a dual career as a biologist, laying down, together with Sewall Wright and J. B. S. Haldane, the foundations of modern theoretical population genetics.

On Student's 1908 Article “The Probable Error of a Mean”

This month marks the 100th anniversary of the appearance of William Sealey Gossets celebrated article, “The Probable Error of a Mean” (Student 1908a). Gossets elegant result represented the first in a series of exact, “small-sample” results that were developed by Gosset, Fisher, and others to form a central component of the modern theory of statistical inference. This review celebrates the centenary of Gossets article by discussing both its background and its impact on statistical theory and practice.

Symmetry and its discontents : essays on the history of inductive probability

Part I. Probability: 1. Symmetry and its discontents 2. The rule of succession 3. Buffon, Price, and Laplace: scientific attribution in the eighteenth century 4. W. E. Johnsons sufficientness postulate. Part II. Personalities: 5 Abraham De Moivre and the birth of the Central Limit Theorem 6 Ramsey, truth, and probability 7. R. A. Fisher on the history of inverse probability 8. R. A. Fisher and the fiducial argument 9. Alan Turing and the Central Limit Theorem Part III. Prediction: 10. Predicting the unpredictable 11. The continuum of inductive methods revised.

Benjamin Peirce and the Howland Will

Abstract 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 Peirces model and discuss the use and abuse of the “product rule” for multiplying probabilities of independent events.

Characterizing Markov exchangeable sequences

In the 1920s the English philosopher W. E. Johnson discovered a simple characterization of the Dirichlet family of conjugate priors for a multinomial distribution having at least three categories. In the present note Johnsons result is extended to the case of a Markov exchangeable sequence.

Time for DNA Disclosure

The legislation that established the U.S. National DNA Index System (NDIS) in 1994 explicitly anticipated that database records would be available for purposes of research and quality control “if personally identifiable information is removed” [42 U.S.C. Sec 14132(b)(3)(D)]. However, the Federal

Babies and the blackout: The genesis of a misconception

Abstract Nine months after the great New York City blackout in November 1965, a series of articles in the New York Times alleged a sharp increase in the citys birthrate. A number of medical and demographic articles then appeared making contradictory (and sometimes erroneous) statements concerning the blackout effect. None of these analyses are fully satisfactory from the statistical standpoint, omitting such factors as weekday-weekend effects, seasonal trends, and a gradual decline in the citys birthrate. Using daily birth statistics for New York City over the 6-year period 1961–1966, techniques of data analysis and time-series analysis are employed in this paper to investigate the above effects.

Carnap and the Logic of Inductive Inference

Publisher Summary This chapter discusses Carnaps work on probability and induction, using the notation and terminology of modern mathematical probability, from the perspective of the modern Bayesian or subjective school of probability. Carnap used logical probability as a tool in understanding the quantitative confirmation of a hypothesis based on evidence and in rational decision making. The resulting analysis of induction involved a two step process. The first step included a broad class of possible confirmation functions, commonly called the “regular c-functions,” along with a unique function in that class (early Carnap) or a parametric family (later Carnap) of specific confirmation functions. The first step in the process essentially placed Carnap in substantial agreement with subjectivists. The second step, however, limits the class of probabilities that distinguishes Carnap from the subjectivist brethren. Carnap largely shaped the way current philosophy views the nature and role of probability, in particular its widespread acceptance of the Bayesian paradigm.

Commentary on Alan M. Turing: The Applications of Probability to Cryptography

Abstract 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 Bayess 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, Turings 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.