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Andrew Gelman - Bayes, statistics, and reproducibility (Rutgers, Foundations of Probability)

Andrew Gelman (Columbia_ January 29, 2018 Title: Bayes, statistics, and reproducibility The two central ideas in the foundations of statistics--Bayesian inference and frequentist evaluation--both are defined in terms of replications. For a Bayesian, the replication comes in the prior distribution, which represents possible parameter values under the set of problems to which a given model might be applied; for a frequentist, the replication comes in the reference set or sampling distribution of possible data that could be seen if the data collection process were repeated. Many serious problems with statistics in practice arise from Bayesian inference that is not Bayesian enough, or frequentist evaluation that is not frequentist enough, in both cases using replication distributions that do not make scientific sense or do not reflect the actual procedures being performed on the data. We consider the implications for the replication crisis in science and discuss how scientists can do better, both in data collection and in learning from the data they have.