
arXiv: 1001.2968
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, Jeffreys 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, however, feel that it is important to understand where our probability models come from, and I welcome the opportunity to use the present article by Robert, Chopin and Rousseau as a platform for further discussion of foundational issues. 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 simplicity; and (3) a key generalization of Jeffreys's ideas is to explicitly include model checking in the process of data analysis.
History of mathematics in the 20th century, FOS: Computer and information sciences, 330, FOS: Political science, Bayesian inference, Statistics, 510, Methodology (stat.ME), Mathematical statistics, History of statistics, FOS: Mathematics, Foundations and philosophical topics in statistics, Political science, Statistics - Methodology
History of mathematics in the 20th century, FOS: Computer and information sciences, 330, FOS: Political science, Bayesian inference, Statistics, 510, Methodology (stat.ME), Mathematical statistics, History of statistics, FOS: Mathematics, Foundations and philosophical topics in statistics, Political science, Statistics - Methodology
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