Extreme data compression for Bayesian model comparison

Journal of Cosmology and Astroparticle Physics, vol. 2023, pp. 048

Abstract

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 corresponding

   Imperial College London

   Affiliation as printed

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

2. Arrykrishna Mootoovaloo corresponding

   University of Oxford

   Affiliation as printed

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

3. Roberto Trotta corresponding

   Scuola Internazionale Superiore di Studi Avanzati · Fondazione ICSC Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing · Imperial College London

   Affiliation as printed

   Centro Nazionale “High Performance Computing, Big Data and Quantum Computing”, Italy

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

   Theoretical and Scientific Data Science, Scuola Internazionale Superiore di Studi Avanzati (SISSA), via Bonomea 265, 34136 Trieste, Italy

4. Elena Sellentin corresponding Aachen Leiden Observatory Mathematical Institute

   Leiden University · Leiden Observatory

   Affiliation as printed

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

   Mathematical Institute, Leiden University, Snellius Gebouw, Niels Bohrweg 1, NL-2333 CA Leiden, The Netherlands