Bayesian astrostatistics: a backward look to the future

TL;DR

This paper reviews the history and misconceptions of Bayesian methods in astrophysics, advocates for hierarchical Bayesian modeling, and recommends reporting likelihood summaries instead of catalogs for survey data.

Contribution

It highlights the importance of multilevel Bayesian modeling in astrophysics and proposes a shift in data reporting practices to improve scientific inference.

Findings

Bayesian methods have grown in astrophysics but face misconceptions.

Hierarchical Bayesian modeling is a promising future direction.

Recommends reporting likelihood functions instead of catalogs.

Abstract

This perspective chapter briefly surveys: (1) past growth in the use of Bayesian methods in astrophysics; (2) current misconceptions about both frequentist and Bayesian statistical inference that hinder wider adoption of Bayesian methods by astronomers; and (3) multilevel (hierarchical) Bayesian modeling as a major future direction for research in Bayesian astrostatistics, exemplified in part by presentations at the first ISI invited session on astrostatistics, commemorated in this volume. It closes with an intentionally provocative recommendation for astronomical survey data reporting, motivated by the multilevel Bayesian perspective on modeling cosmic populations: that astronomers cease producing catalogs of estimated fluxes and other source properties from surveys. Instead, summaries of likelihood functions (or marginal likelihood functions) for source properties should be reported (not posterior probability density functions), including nontrivial summaries (not simply upper limits) for candidate objects that do not pass traditional detection thresholds.