Efficient prior sensitivity analysis for Bayesian model comparison

TL;DR

This paper introduces a computationally efficient method for prior sensitivity analysis in Bayesian model comparison by leveraging the learned harmonic mean estimator, reducing costs significantly while maintaining accuracy.

Contribution

It presents a novel approach that decouples sampling from evidence calculation, enabling fast prior sensitivity analysis without additional model re-fits or specialized sampling.

Findings

Achieves up to 6000x reduction in computational cost in a cosmological case study.

Reproduces results of full MCMC and nested sampling with less computation.

Validated on toy problems and real-world data.

Abstract

Bayesian model comparison implements Occam's razor through its sensitivity to the prior. However, prior-dependence makes it important to assess the influence of plausible alternative priors. Such prior sensitivity analyses for the Bayesian evidence are expensive, either requiring repeated, costly model re-fits or specialised sampling schemes. By exploiting the learned harmonic mean estimator (LHME) for evidence calculation we decouple sampling and evidence calculation, allowing resampled posterior draws to be used directly to calculate the evidence without further likelihood evaluations. This provides an alternative approach to prior sensitivity analysis for Bayesian model comparison that dramatically alleviates the computational cost and is agnostic to the method used to generate posterior samples. We validate our method on toy problems and a cosmological case study, reproducing estimates obtained by full Markov chain Monte Carlo (MCMC) sampling and nested sampling re-fits. For the cosmological example considered our approach achieves up to $6000\times$ lower computational cost.