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Jack: The Good Zoroastrian, by Nozer D. Singpurwalla

Module by: David Banks, eric smith. E-mail the authorsEdited By: Ben Allen, David Banks, Frederick Moody, eric smith

Summary: An appreciation of the work of the legendary I.J. Good, one of the world's leading statisticians. This essay is included in The Good Book: Thirty Years of Comments, Conjectures and Conclusions by I.J. Good, available in print from Rice University Press (http://ricepress.rice.edu).

(This module helps introduce The Good Book: Thirty Years of Comments, Conjectures and Conclusions, by I.J. Good. The book is available for purchase from the Rice University Press Store. You can also visit the Rice University Press web site.)

Irving John Good: The Man

Humata, Hukhta and Hvarshta are the three guiding principles of Zoroastrianism, a philosophical conception of deity that came out of Persia before the time of Christ. Translated from the ancient language of Avesta, these words mean Good Thoughts, Good Words, and Good Deeds.

Jack Good, a mathematician, a statistician, a computer scientist, a philosopher, and a chess expert, is well known for his good thoughts. One only need read Good (1983) on Good Thinking: The Foundations of Probability and Its Applications. On the matter of Good Words, those of us fortunate to know Jack cannot recall having heard him utter an unkind word or a disparaging comment about anyone. A possible exception could be Good (1990), wherein he calls R. A. Fisher “... a great practitioner but a mediocre philosopher.” Finally, on the matter of Good Deeds, what can be better than a Good-like deed of generously citing the work of other colleagues, no matter how inconsequential the work? Jack therefore fully deserves the accolade of being called “The Good Zoroastrian,” or paraphrasing Rudyard Kipling, “You are a better Zoroastrian than I, Irving John.”

Jack Good: An Appreciation

David Banks wanted of me an “appreciation” of Jack's work. By this I am presuming that David wanted me to reflect on the impact of Jack's writings on reliability, survival analysis, and quality control, broadly labeled the assurance sciences. I am grateful to David for this opportunitybecause it motivated me to re-visit some of Jack's writings, beginning with his earliest on Probability and the Weighing of Evidence (1950), to one of his latest on “Subjective Probability” (1990). Sandwiched between these is an impressive list of over two thousand articles and books, some of the more notable ones (to me) being “Rational Decisions” (1952), “A Theory of Causality” (1959), “The Estimation of Probabilities” (1965), “A Subjective Evaluation of Bode's Law” (1969), “Dynamic Probability, Computer Chess, and the Measurement of Knowledge” (1977), “Some History of the Hierarchical Bayesian Methodology” (1981), and then of course such titillating titles as “Quantum Mechanics and Yoga” (1963), and “Good Saw That It Was God(d)” (1975). But since my present charge is to focus on the assurance sciences, I will, in what follows, say a few words about this.

Traditionally, and up until recently, the point of view adopted by most reliability theorists and life data analysts is that reliability is a probability. The fact that there could be different kinds of probability has been an alien concept, and continues to be so in survival analysis. In Good (1965), the different interpretations of probability are carefully articulated. These are: chance or propensity (a physical probability), psychological probability, subjective probability, and credibility (or a logical probability). In Good (1990), the focus is on subjective probability; also given there is a dendroidal classification of the different kinds of probability and usages of the term. A consequence of these writings, together with those of de Finetti, Savage, and Lindley, is that reliability is now seen as an unknown chance (or propensity), and one's uncertainty about the reliability, expressed as a personal probability, is labelled survivability [cf. Singpurwalla (2006), “Reliability and Risk: A Bayesian Perspective”].

This distinction between reliability and survivability has far-reaching ramifications. For one, it makes survivability assessments dynamic. For another, it brings into play the hierarchical nature of probabilities (first via chance, and then via a subjective probability imposed on chance). Finally, it imparts a sense of truthfulness in the context of life-time assessments, because in actuality one ends obtaining an item's survivability, not its reliability. The former is personal and subjective; the latter is abstract and unobservable. Hierarchical probabilities also come into play when assessing network and system integrity. Good has commented on the hierarchical and dynamic nature of probability as early as 1965 and perhaps earlier.

The impact of Good's other works on the assurance sciences pertains to acceptance sampling based on life-test data using the weighing of evidence concept via Bayes' Factors, information gleaned from life test data and the design of life testing experiments, and the classification of interdependent failures as being cascading or causal. Good's discussion of rational behavior and the utility of a distribution [Good (1968)] takes a tangible form when one needs to apportion reliability between the nodes of a network and when one needs to choose systems with competing designs. For a flavor of these topics, see Singpurwalla (2006) and the references therein.

All in all, Good's writings are so plentiful and so diverse that one can find their impact on a wide variety of topics in mathematics, statistics, operations research, philosophy, psychology, parapsychology, physics, and even yoga! For this broad body of work, Jack deserves deep appreciation from us all for his contributions to our learning.

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