Quantifying and mitigating bias in inference on gravitational wave source populations

TL;DR

This paper analyzes how model inaccuracies bias gravitational wave source population inferences and demonstrates that Gaussian process likelihoods can effectively reduce this bias, improving the reliability of population studies.

Contribution

It derives an analytic approximation for the bias in population inference due to model errors and shows how Gaussian process likelihoods mitigate this bias.

Findings

Bias in population inference is quantifiable with the derived approximation.

Gaussian process likelihoods reduce bias caused by model inaccuracies.

Mitigation methods improve the reliability of gravitational wave population analyses.

Abstract

When using incorrect or inaccurate signal models to perform parameter estimation on a gravitational wave signal, biased parameter estimates will in general be obtained. For a single event this bias may be consistent with the posterior, but when considering a population of events this bias becomes evident as a sag below the expected diagonal line of the P-P plot showing the fraction of signals found within a certain significance level versus that significance level. It would be hoped that recently proposed techniques for accounting for model uncertainties in parameter estimation would, to some extent, alleviate this problem. Here we demonstrate that this is indeed the case. We derive an analytic approximation to the P-P plot obtained when using an incorrect signal model to perform parameter estimation. This approximation is valid in the limit of high signal-to-noise ratio and nearly correct waveform models. We show how the P-P plot changes if a Gaussian process likelihood that allows for model errors is used to analyse the data. We demonstrate analytically and using numerical simulations that the bias is always reduced in this way. These results provide a way to quantify bias in inference on populations and demonstrate the importance of utilising methods to mitigate this bias.