Extracting distribution parameters from multiple uncertain observations with selection biases

TL;DR

This paper presents a Bayesian method to accurately infer population distribution parameters from biased and uncertain observational data, demonstrated with gravitational-wave astrophysics.

Contribution

It introduces a novel Bayesian framework that accounts for measurement uncertainties and selection biases in population analyses.

Findings

Successfully extracts mass ratio distribution from biased gravitational-wave data.

Demonstrates robustness of the method with substantial measurement uncertainties.

Provides a practical approach for population inference under selection effects.

Abstract

We derive a Bayesian framework for incorporating selection effects into population analyses. We allow for both measurement uncertainty in individual measurements and, crucially, for selection biases on the population of measurements, and show how to extract the parameters of the underlying distribution based on a set of observations sampled from this distribution. We illustrate the performance of this framework with an example from gravitational-wave astrophysics, demonstrating that the mass ratio distribution of merging compact-object binaries can be extracted from Malmquist-biased observations with substantial measurement uncertainty.