2013/01/01 by Farhan Feroz, F. Feroz, John Skilling +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Artificial intelligence #Bayesian probability #Computer science #Gaussian Processes and Bayesian Inference #Gibbs sampling #Markov Chains and Monte Carlo Methods #Markov chain Monte Carlo #Mathematical optimization #Mathematics #Monte Carlo method #Posterior probability #Sampling (signal processing) #Slice sampling #Statistical Methods and Bayesian Inference #Statistics #astro-ph.IM #physics.data-an #stat.CO
paper · pdf · doi:10.1063/1.4819989
published as AIP Conference Proceedings, Volume 1553, pp. 106-113 (2013) · Refereed conference proceeding, presented at 32nd International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering
openalex publication_date 2013/01/01 · arxiv created 2013/12/19 · arxiv updated 2013/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Abstract. In performing a Bayesian analysis, two difficult problems often emerge. First, in es-timating the parameters of some model for the data, the resulting posterior distribution may be multi-modal or exhibit pronounced (curving) degeneracies. Secondly, in selecting between a set of competing models, calculation of the Bayesian evidence for each model is computationally ex-pensive using existing methods such as thermodynamic integration. Nested Sampling is a Monte Carlo method targeted at the efficient calculation of the evidence, but also produces posterior in-ferences as a by-product and therefore provides means to carry out parameter estimation as well as model selection. The main challenge in implementing Nested Sampling is to sample from a con-strained probability distribution. One possible solution to this problem is provided by the Galilean Monte Carlo (GMC) algorithm. We show results of applying Nested Sampling with GMC to some problems which have proven very difficult for standard Markov Chain Monte Carlo (MCMC) and down-hill methods, due to the presence of large number of local minima and/or pronounced (curv-ing) degeneracies between the parameters. We also discuss the use of Nested Sampling with GMC in Bayesian object detection problems, which are inherently multi-modal and require the evaluation of Bayesian evidence for distinguishing between true and spurious detections.