Extreme data compression for Bayesian model comparison

TL;DR

This paper introduces an extreme data compression technique using the MOPED algorithm for Bayesian model comparison, which maintains accuracy while significantly reducing computational costs.

Contribution

It demonstrates that MOPED-based data compression preserves Bayes factors in linear Gaussian models and shows negligible differences in nonlinear cases, improving computational efficiency.

Findings

Bayes factors are identical in linear Gaussian models using MOPED.

Negligible differences in nonlinear models' Bayes factors with compression.

Compression reduces sampling variance of the Evidence without affecting Bayes factors.

Abstract

We develop extreme data compression for use in Bayesian model comparison via the MOPED algorithm, as well as more general score compression. We find that Bayes factors from data compressed with the MOPED algorithm are identical to those from their uncompressed datasets when the models are linear and the errors Gaussian. In other nonlinear cases, whether nested or not, we find negligible differences in the Bayes factors, and show this explicitly for the Pantheon-SH0ES supernova dataset. We also investigate the sampling properties of the Bayesian Evidence as a frequentist statistic, and find that extreme data compression reduces the sampling variance of the Evidence, but has no impact on the sampling distribution of Bayes factors. Since model comparison can be a very computationally-intensive task, MOPED extreme data compression may present significant advantages in computational time.