A comparison of Bayesian sampling algorithms for high-dimensional particle physics and cosmology applications

Computer Physics Communications, vol. 315, pp. 109756

Abstract

For several decades now, Bayesian inference techniques have been applied to theories of particle physics, cosmology and astrophysics to obtain the probability density functions of their free parameters. In this study, we review and compare a wide range of Markov chain Monte Carlo (MCMC) and nested sampling techniques to determine their relative efficacy on functions that resemble those encountered most frequently in the particle astrophysics literature. Our first series of tests explores a series of high-dimensional analytic test functions that exemplify particular challenges, for example highly multimodal posteriors or posteriors with curving degeneracies. We then investigate two real physics examples, the first being a global fit of the Λ CDM model using cosmic microwave background data from the Planck experiment, and the second being a global fit of the Minimal Supersymmetric Standard Model using a wide variety of collider and astrophysics data. We show that several examples widely thought to be most easily solved using nested sampling approaches can in fact be more efficiently solved using modern MCMC algorithms, but the details of the implementation matter. Furthermore, we also provide a series of useful insights for practitioners of particle astrophysics and cosmology.

Authors 7

1. Joshua G. Albert Aachen Leiden Observatory

   Leiden University · California Institute of Technology · Leiden Observatory

   Affiliation as printed

   Cahill Center for Astronomy and Astrophysics, California Institute of Technology, Pasadena, CA 91125, USA

   Leiden Observatory, Leiden University, PO Box 9513, 2300 Leiden, the Netherlands

2. Csaba Balázs

   Monash University

   Affiliation as printed

   School of Physics and Astronomy, Monash University, Melbourne, VIC 3800, Australia

3. Andrew Fowlie

   Xi’an Jiaotong-Liverpool University

   Affiliation as printed

   Department of Physics, School of Mathematics and Physics, Xi'an Jiaotong-Liverpool University, Suzhou, 215123, China

4. Will J. Handley

   University of Cambridge

   Affiliation as printed

   Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge, CB3 0HE, UK

   Kavli Institute for Cosmology, Madingley Road, Cambridge, CB3 0HA, UK

5. N. T. Hunt-Smith corresponding

   The University of Adelaide

   Affiliation as printed

   ARC Centre for Dark Matter Particle Physics, Department of Physics, University of Adelaide, Adelaide, SA 5005, Australia

6. Roberto Ruiz de Austri
7. Martin J. White

   The University of Adelaide

   Affiliation as printed

   ARC Centre for Dark Matter Particle Physics, Department of Physics, University of Adelaide, Adelaide, SA 5005, Australia