The prior can generally only be understood in the context of the likelihood

2017/08/24 by Andrew Gelman, Daniel Simpson, Michael Betancourt · 2 voices · 459 citations
Decision Sciences · Mathematics · #Bayesian inference #Bayesian probability #Context (archaeology) #Entropy (arrow of time) #Inference #Key (lock) #Principle of maximum entropy #Prior probability #Psychometric Methodologies and Testing #Statistical Distribution Estimation and Applications #Statistical Methods and Bayesian Inference #stat.ME

paper · pdf · open access · doi:10.3390/e19100555

published in Entropy 19(10), 555 (Multidisciplinary Digital Publishing Institute) · 13 pages

arxiv created 2017/08/31 · openalex created_date 2017/08/31 · openalex publication_date 2017/10/19 · arxiv updated 2017/11/22 · openalex updated_date 2026/08/05

Abstract

A key sticking point of Bayesian analysis is the choice of prior distribution, and there is a vast literature on potential defaults including uniform priors, Jeffreys' priors, reference priors, maximum entropy priors, and weakly informative priors. These methods, however, often manifest a key conceptual tension in prior modeling: a model encoding true prior information should be chosen without reference to the model of the measurement process, but almost all common prior modeling techniques are implicitly motivated by a reference likelihood. In this paper we resolve this apparent paradox by placing the choice of prior into the context of the entire Bayesian analysis, from inference to prediction to model evaluation.

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Discussions

• The prior can generally only be understood in the context of the likelihood [hn, 94 points, 20 comments]
• The degree to which a prior is informative depends on the likelihood 🤷‍♂️ arxiv.org/abs/1708.07487 [bsky, 4 points, 1 comments]

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