Eur. Phys. J. C (2017) 77: 761
https://doi.org/10.1140/epjc/s10052-017-5274-y

Special Article - Tools for Experiment and Theory

Comparison of statistical sampling methods with ScannerBit, the GAMBIT scanning module

¹ Physics and Astronomy Department, University of California, Los Angeles, CA, 90095, USA
² Department of Physics, Blackett Laboratory, Imperial College London, Prince Consort Road, London, SW7 2AZ, UK
³ Oskar Klein Centre for Cosmoparticle Physics, AlbaNova University Centre, 10691, Stockholm, Sweden
⁴ Department of Physics, Stockholm University, 10691, Stockholm, Sweden
⁵ Department of Physics, McGill University, 3600 rue University, Montreal, QC, H3A 2T8, Canada
⁶ LAPTh, Université de Savoie, CNRS, 9 chemin de Bellevue B.P.110, 74941, Annecy-le-Vieux, France

^* e-mail: p.scott@imperial.ac.uk

Received: 14 March 2017
Accepted: 2 October 2017
Published online: 13 November 2017

Abstract

We introduce ScannerBit, the statistics and sampling module of the public, open-source global fitting framework GAMBIT. ScannerBit provides a standardised interface to different sampling algorithms, enabling the use and comparison of multiple computational methods for inferring profile likelihoods, Bayesian posteriors, and other statistical quantities. The current version offers random, grid, raster, nested sampling, differential evolution, Markov Chain Monte Carlo (MCMC) and ensemble Monte Carlo samplers. We also announce the release of a new standalone differential evolution sampler, Diver, and describe its design, usage and interface to ScannerBit. We subject Diver and three other samplers (the nested sampler MultiNest, the MCMC GreAT, and the native ScannerBit implementation of the ensemble Monte Carlo algorithm T-Walk) to a battery of statistical tests. For this we use a realistic physical likelihood function, based on the scalar singlet model of dark matter. We examine the performance of each sampler as a function of its adjustable settings, and the dimensionality of the sampling problem. We evaluate performance on four metrics: optimality of the best fit found, completeness in exploring the best-fit region, number of likelihood evaluations, and total runtime. For Bayesian posterior estimation at high resolution, T-Walk provides the most accurate and timely mapping of the full parameter space. For profile likelihood analysis in less than about ten dimensions, we find that Diver and MultiNest score similarly in terms of best fit and speed, outperforming GreAT and T-Walk; in ten or more dimensions, Diver substantially outperforms the other three samplers on all metrics.