Monday, August 22, 2011

46,656 Varieties of Bayesianism (at least)

Legal theorists sometimes speak of "the" Bayesian interpretation of evidence, inference, proof, and probability. However, see Sharon Bertsch McGrayne, The Theory That Would Not Die 129 (Yale 2011):
Bayesian theories mushroomed in glorious profusion during the 1960s, and Jack Good claimed he counted "at least 46656 different interpretations," far more than the world had statisticians.1 [1. I.J. Good, "46656 Varieties of Bayesianism," Letter to the Editor, 25 American Statistician 62-63 (1971).] Version included subjective, personalist, objective, empirical Bayes (EB for short), semi-EB, semi-Bayes, epistemic, intuitionist, logical, fuzzy, hierarchical, pseudo, quasi, compound, parametric, nonparametric, hyperparametric, and non-hyperparametric Bayes. ... When asked how to differentiate one Bayesian from another, a biostatistician cracked, "Ye shall know them by their posteriors."
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