I count Jack Good among my friends, He corresponded with me during the 1970s about cryptanalysis, shrinkage estimators for multinomial cell probabilities, and density estimation and bumping hunting using roughness penalties, We met at Valencia 1 in 1979, and then several times in the United States. He was very supportive of my research, and we played chess together. He and Morris De Groot were for me the truly great men of post-Turing Bayesian Statistics
JACK GOOD, IN MEMORIUM
An excerpt from THE LIFE OF A BAYESIAN BOY (CHAPTER 3)
Within a few weeks I was able to extend Dennis’s method for the estimation of several exchangeable means and variances (that he’d extended to M-group regression in Iowa City during a remunerative consultancy for the American College Testing program with Mel Novick) to simultaneous inference and shrinkage estimation for several binomial probabilities. I did this by employing logistic transformations and non-conjugate hierarchical prior distributions, and these devices lead to my very first paper in an international journal (Bayesian Methods for Binomial Data, Biometrika 1972).
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My friend Irving Jack Good (with whom I corresponded about Alan Turing and their multinomial shrinkage estimators for cryptanalysis at Bletchley Park, which were instrumental in solving the Nazi codes) did not believe that my more general Logit/ First Stage Multivariate Normal Prior / hierarchical approach to the analysis of categorical data was sufficiently recognised by other Bayesians. Nevertheless, Alan Agresti and several other authors seem to think that it was a pioneering contribution, along with my external examiner’s (Patricia Altham’s) novel analysis of measures of association for 2x2 contingency tables. Indeed, many others have followed in my footsteps.
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Related Work: EDWARD SIMPSON, BAYES AT BLETCHLEY PARK
TURING, BAYES AT BLETCHLEY PARK
An excerpt from A PERSONAL HISTORY OF BAYESIAN STATISTICS Chapter 4
n their 1973 JASA paper, Stephen Fienberg and Paul Holland proposed Empirical Bayes alternatives to Jack Good’s 1965 hierarchical Bayes estimators for p multinomial cell probabilities. They devised a ratio-unbiased data-based estimate for Good’s flattening constant α, and proved that the corresponding shrinkage estimators for the cell probabilities possess outstanding mean squared error properties for large enough p. Fienberg and Holland show that, while the sample proportions are admissible with respect to squared error loss, they possess quite inferior risk properties on the interior of parameter space when p is large, a seminal result.
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