2020/02/29 by Andrew Gelman, Yuling Yao · 18 citations
Arts and Humanities · Mathematics · Physics and Astronomy · #Artificial intelligence #Bayes factor #Bayesian average #Bayesian experimental design #Bayesian inference #Bayesian probability #Bayesian programming #Bayesian statistics #Computer science #Frequentist inference #Machine learning #Mathematics #Philosophy and History of Science #Prior probability #Probability and Statistical Research #Quantum Mechanics and Applications #math.ST #stat.ME #stat.TH
paper · pdf · doi:10.1088/1361-6471/abc3a5
published in Journal of Physics G Nuclear and Particle Physics 48(1), 014002 (IOP Publishing) · To appear in Journal of Physics G
openalex created_date 2020/02/24 · openalex publication_date 2020/10/21 · arxiv created 2020/11/10 · arxiv updated 2020/11/12 · openalex updated_date 2026/08/06
Abstract Every philosophy has holes, and it is the responsibility of proponents of a philosophy to point out these problems. Here are a few holes in Bayesian data analysis: (1) the usual rules of conditional probability fail in the quantum realm, (2) flat or weak priors lead to terrible inferences about things we care about, (3) subjective priors are incoherent, (4) Bayesian decision picks the wrong model, (5) Bayes factors fail in the presence of flat or weak priors, (6) for Cantorian reasons we need to check our models, but this destroys the coherence of Bayesian inference. Some of the problems of Bayesian statistics arise from people trying to do things they should not be trying to do, but other holes are not so easily patched. In particular, it may be a good idea to avoid flat, weak, or conventional priors, but such advice, if followed, would go against the vast majority of Bayesian practice and requires us to confront the fundamental incoherence of Bayesian inference. This does not mean that we think Bayesian inference is a bad idea, but it does mean that there is a tension between Bayesian logic and Bayesian workflow which we believe can only be resolved by considering Bayesian logic as a tool, a way of revealing inevitable misfits and incoherences in our model assumptions, rather than as an end in itself.