Extreme data compression for Bayesian model comparison

arXiv (Cornell University)

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.

Authors 4

1. Alan Heavens

   Imperial College London

   Affiliation as printed

   Imperial Centre for Inference and Cosmology (ICIC) , Department of Physics , Imperial Col- lege , Blackett Laboratory , Prince Consort Road , London SW7 2AZ , U.K

2. Arrykrishna Mootoovaloo

   University of Oxford

   Affiliation as printed

   Department of Physics , University of Oxford , Denys Wilkinson Building , Keble Road , Ox- ford OX1 3RH , U.K

3. Roberto Trotta
4. Elena Sellentin Aachen Leiden Observatory

   Leiden University · Leiden Observatory

   Affiliation as printed

   Leiden Observatory , Leiden University , Oort Gebouw , Niels Bohrweg 2 , NL-2333 CA Leiden , The Netherlands