Accounting for sample selection in Bayesian analyses

TL;DR

This paper introduces Bayesian methods to correct for sample selection biases in astronomical data, using analytic approximations and Monte Carlo integration, with broad applicability across fields facing similar issues.

Contribution

It provides a unified Bayesian framework with practical solutions for both tractable and intractable models, including sample correction techniques and implementation guidance.

Findings

Effective correction for sample selection biases demonstrated with toy models

Method applicable to data truncation and impure samples

Sample code provided for practical implementation

Abstract

Astronomers are often confronted with funky populations and distributions of objects: brighter objects are more likely to be detected; targets are selected based on colour cuts; imperfect classification yields impure samples. Failing to account for these effects leads to biased analyses. In this paper we present a simple overview of a Bayesian consideration of sample selection, giving solutions to both analytically tractable and intractable models. This is accomplished via a combination of analytic approximations and Monte Carlo integration, in which dataset simulation is efficiently used to correct for issues in the observed dataset. This methodology is also applicable for data truncation, such as requiring densities to be strictly positive. Toy models are included for demonstration, along with discussions of numerical considerations and how to optimise for implementation. We provide sample code to demonstrate the techniques. The methods in this paper should be widely applicable in fields beyond astronomy, wherever sample selection effects occur.