Practical Guidance for Bayesian Inference in Astronomy

arXiv (Cornell University)

Abstract

In the last two decades, Bayesian inference has become commonplace in astronomy. At the same time, the choice of algorithms, terminology, notation, and interpretation of Bayesian inference varies from one sub-field of astronomy to the next, which can lead to confusion to both those learning and those familiar with Bayesian statistics. Moreover, the choice varies between the astronomy and statistics literature, too. In this paper, our goal is two-fold: (1) provide a reference that consolidates and clarifies terminology and notation across disciplines, and (2) outline practical guidance for Bayesian inference in astronomy. Highlighting both the astronomy and statistics literature, we cover topics such as notation, specification of the likelihood and prior distributions, inference using the posterior distribution, and posterior predictive checking. It is not our intention to introduce the entire field of Bayesian data analysis -- rather, we present a series of useful practices for astronomers who already have an understanding of the Bayesian "nuts and bolts" and wish to increase their expertise and extend their knowledge. Moreover, as the field of astrostatistics and astroinformatics continues to grow, we hope this paper will serve as both a helpful reference and as a jumping off point for deeper dives into the statistics and astrostatistics literature.

Authors 8

1. Gwendolyn M. Eadie

   University of Toronto

   Affiliation as printed

   University of Toronto , David A. Dunlap Department of Astronomy & Astrophysics , Toronto , M5S 3H4 , Canada

   University of Toronto , Department of Statistical Sciences , Toronto , M5S 3G3 , Canada

2. Joshua S. Speagle
3. Jessi Cisewski-Kehe

   University of Wisconsin–Madison

   Affiliation as printed

   University of Wisconsin-Madison , Department of Statistics , Madison , WI , 53706 , USA

4. Daniel T. Foreman-Mackey

   Flatiron Institute

   Affiliation as printed

   Center for Computational Astrophysics , Flatiron Institute , 160 5th Ave , New York , NY 10010 , USA

5. Daniela Huppenkothen Aachen SRON Netherlands Institute for Space Research

   Space Research Organisation Netherlands

   Affiliation as printed

   SRON Netherlands Institute for Space Research , Niels Bohrlaan 4 , 2333 CA Leiden , Netherlands

6. David E. Jones

   Texas A&M University

   Affiliation as printed

   Texas A&M University , Department of Statistics , College Station , TX 77843 , USA

7. Aaron Springford
   Affiliation as printed

   Cytel , Toronto , Ontario , Canada

8. Hyungsuk Tak