🤖 AI Summary
This work addresses the computational burden of prior sensitivity analysis in Bayesian model comparison, which is highly sensitive to prior choice yet traditionally requires repeated model refitting. We introduce, for the first time, the Learned Harmonic Mean Estimator (LHME) to this task, decoupling posterior sampling from marginal likelihood computation. This enables efficient evaluation of Bayesian evidence under multiple priors using a single set of posterior samples, eliminating the need for re-fitting and remaining agnostic to the underlying inference algorithm. In a cosmological case study, our approach achieves speedups of up to 6,000-fold compared to conventional methods while yielding results consistent with those obtained via MCMC and nested sampling.
📝 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.