Getting Bayesian ideas across to a wide audience

George Cowgill

«Archeologia e Calcolatori» 2002, 13, 191-196

Abstract

A generally Bayesian attitude toward statistical inference seems to me so obviously superior to the 'classical' Neyman-Pearson approach that it is difficult to comprehend why not everyone agrees. I believe that most non-statisticians learn classical procedures ritualistically but then interpret their results in naively Bayesian ways. It would be better if they became more sophisticated and knowing Bayesians. A truly introductory text on the logic of Bayesian inference, with some simple but useful applications, would probably help. Bayesian inference with an uninformative prior may yield the same results as classical inference, but with coherent rather than muddled logic. An example of a very useful but mathematically simple archaeological application of an informative prior is using prior information to improve estimates of true proportions of artifact categories in populations represented by small collections. However, a complication arises when the observed proportion in a fairly large sample is well outside the range considered at all likely for the relevant population, based on prior information. In this case, straightforward use of a beta prior distribution can yield results that seem unreasonable. Possibly our prior information is better represented by a modified beta distribution with 'heavy' tails. Advice about this problem would be appreciated.

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