The Prior Can Often Only Be Understood in the Context of the Likelihood

Gelman, Andrew; Simpson, Daniel; Betancourt, Michael

doi:10.3390/e19100555

Open AccessArticle

The Prior Can Often Only Be Understood in the Context of the Likelihood

by

Andrew Gelman

^1,2,*

,

Daniel Simpson

³ and

Michael Betancourt

⁴

¹

Department of Statistics, Columbia University, New York, NY 10027, USA

²

Department of Political Science, Columbia University, New York, NY 10027, USA

³

Department of Statistical Sciences, University of Toronto, Toronto, ON M5S, Canada

⁴

Institute for Social and Economic Research and Policy, Columbia University, New York, NY 10027, USA

^*

Author to whom correspondence should be addressed.

Entropy 2017, 19(10), 555; https://doi.org/10.3390/e19100555

Submission received: 26 August 2017 / Revised: 30 September 2017 / Accepted: 14 October 2017 / Published: 19 October 2017

(This article belongs to the Special Issue Maximum Entropy and Bayesian Methods)

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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.

Keywords: Bayesian inference; default priors; prior distribution

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MDPI and ACS Style

Gelman, A.; Simpson, D.; Betancourt, M. The Prior Can Often Only Be Understood in the Context of the Likelihood. Entropy 2017, 19, 555. https://doi.org/10.3390/e19100555

AMA Style

Gelman A, Simpson D, Betancourt M. The Prior Can Often Only Be Understood in the Context of the Likelihood. Entropy. 2017; 19(10):555. https://doi.org/10.3390/e19100555

Chicago/Turabian Style

Gelman, Andrew, Daniel Simpson, and Michael Betancourt. 2017. "The Prior Can Often Only Be Understood in the Context of the Likelihood" Entropy 19, no. 10: 555. https://doi.org/10.3390/e19100555

APA Style

Gelman, A., Simpson, D., & Betancourt, M. (2017). The Prior Can Often Only Be Understood in the Context of the Likelihood. Entropy, 19(10), 555. https://doi.org/10.3390/e19100555

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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The Prior Can Often Only Be Understood in the Context of the Likelihood

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