Practical Guidance for Bayesian Inference in Astronomy

In the last two decades, Bayesian inference has become commonplace in astronomy, but terminology, notation, algorithm choices, and interpretations vary across sub-fields and between astronomy and statistics, causing confusion. This paper aims to (1) consolidate and clarify terminology and notation across disciplines, and (2) outline practical guidance for Bayesian inference in astronomy. Highlighting both astronomy and statistics literature, the authors cover notation, specification of the likelihood and prior distributions, inference using the posterior distribution, and posterior predictive checking. The article targets astronomers already familiar with Bayesian basics who wish to deepen their expertise. Using a running parallax-based distance inference example, it identifies common pitfalls and promotes best practices, serving as a reference and a springboard for deeper dives into the literature.