Bayes, Jeffreys, Prior Distributions and the Philosophy of Statistics

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Bayes, Jeffreys, Prior Distributions and the Philosophy of Statistics 1 Andrew Gelman I actually own a copy of Harold Jeffreys's Theory of Probability but have only read small bits of it, most recently over a decade ago to confirm that, indeed, Jef-freys was not too proud to use a classical chi-squared p-value when he wanted to check the misfit of a model to data (Gelman, Meng and Stern, 2006). I do, how-ever, feel that it is important to understand where our probability models come from, and I welcome the op-portunity to use the present article by Robert, Chopin and Rousseau as a platform for further discussion of foundational issues. 2 In this brief discussion I will argue the following: (1) in thinking about prior distributions, we should go beyond Jeffreys's principles and move toward weakly informative priors; (2) it is natural for those of us who work in social and computational sciences to favor complex models, contra Jeffreys's preference for sim-plicity; and (3) a key generalization of Jeffreys's ideas is to explicitly include model checking in the process of data analysis.

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