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Importance NestedSampling and theMultiNest Algorithm Farhan FerozM. P. HobsonEwan Cameron2019 год

Importance Nested Sampling and the MultiNest Algorithm
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Аннотация: Bayesian inference involves two main computational challenges. First, in estimating the parameters of some model for the data, the posterior distribution may well be highly multi-modal: a regime in which the convergence to stationarity of traditional Markov Chain Monte Carlo (MCMC) techniques becomes incredibly slow. Second, in selecting between a set of competing models the necessary estimation of the Bayesian evidence for each is, by definition, a (possibly high-dimensional) integration over the entire parameter space; again this can be a daunting computational task, although new Monte Carlo (MC) integration algorithms offer solutions of ever increasing efficiency. Nested sampling (NS) is one such contemporary MC strategy targeted at calculation of the Bayesian evidence, but which also enables posterior inference as a by-product, thereby allowing simultaneous parameter estimation and model selection. The widely-used MultiNest algorithm presents a particularly efficient implementation of the NS technique for multi-modal posteriors. In this paper we discuss importance nested sampling (INS), an alternative summation of the MultiNest draws, which can calculate the Bayesian evidence at up to an order of magnitude higher accuracy than `vanilla' NS with no change in the way MultiNest explores the parameter space. This is accomplished by treating as a (pseudo-)importance sample the totality of points collected by MultiNest, including those previously discarded under the constrained likelihood sampling of the NS algorithm. We apply this technique to several challenging test problems and compare the accuracy of Bayesian evidences obtained with INS against those from vanilla NS.
Год издания: 2019
Авторы: Farhan Feroz, M. P. Hobson, Ewan Cameron, A. N. Pettitt
Источник: The Open Journal of Astrophysics
Ключевые слова: Statistical Methods and Bayesian Inference, Markov Chains and Monte Carlo Methods, Statistical Methods and Inference
Другие ссылки: The Open Journal of Astrophysics (PDF)
The Open Journal of Astrophysics (HTML)
DOAJ (DOAJ: Directory of Open Access Journals) (HTML)
arXiv (Cornell University) (PDF)
arXiv (Cornell University) (HTML)
arXiv (Cornell University) (PDF)
arXiv (Cornell University) (HTML)
DataCite API (HTML)