Comparison of statistical sampling methods with ScannerBit, the GAMBIT scanning module
Gregory D. Martinez (Physics and Astronomy Department, University of California, 0000 0000 9632 6718, 90095, Los Angeles, CA, USA); James McKay (Department of Physics, Blackett Laboratory, Imperial College London, 0000 0001 2113 8111, Prince Consort Road, SW7 2AZ, London, UK); Ben Farmer (Oskar Klein Centre for Cosmoparticle Physics, AlbaNova University Centre, 0000 0004 0512 3288, 10691, Stockholm, Sweden, Department of Physics, Stockholm University, 0000 0004 1936 9377, 10691, Stockholm, Sweden); Pat Scott (Department of Physics, Blackett Laboratory, Imperial College London, 0000 0001 2113 8111, Prince Consort Road, SW7 2AZ, London, UK); Elinore Roebber (Department of Physics, McGill University, 0000 0004 1936 8649, 3600 rue University, H3A 2T8, Montreal, QC, Canada); et al - Show all 7 authors
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.
