Importance Nested Sampling and the MultiNest Algorithm

By Farhan Feroz, M. Hobson, Ewan Cameron, Anthony N. Pettitt. The Open Journal of Astrophysics, 2013

693 citations recorded by the source corpus.

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.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2dfa9451a1b6a6d88ad574f29298ce7e6c117052

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Citations in the corpus

Retrieving scattering clouds and disequilibrium chemistry in the atmosphere of HR 8799e (2020, methodology): “…and disequilibrium chemistry in the atmosphere of HR 8799e To derive the posterior abundances of our fit we used the PyMultiNest5 package (Buchner et al. 2014), which is a Python wrapper of the MultiNest method (Feroz & Hobson 2008; Feroz et al. 2009, 2019) for nested sampling (Skilling 2004).”
Planck2018 results (2018, methodology): “In the Bayesian approach, a feature model’s general performance relative to base ΛCDM can be expressed in terms of the Bayesian evidence E (Trotta 2007a), which is also evaluated by MultiNest.”
IceCube high-energy starting event sample: Description and flux characterization with 7.5 years of data (2020, methodology): “To compute the model evidence, we use the MultiNest package [158].”
An Updated Mass–Radius Analysis of the 2017–2018 NICER Data Set of PSR J0030+0451 (2023, methodology): “Such a signal is generated for every parameter vector sampled by MULTINEST ( Feroz & Hobson 2008; Feroz et al. 2009, 2019 ) , the algorithm adopted within X-PSI to explore the model parameter space through a nested sampling algorithm ( Skilling 2004 ) .”
H2O abundances and cloud properties in ten hot giant exoplanets (2018, methodology): “The statistical framework uses the MultiNest nested sampling technique that enables model parameter estimation and calculation of the Bayesian evidence (Skilling 2004; Feroz & Hobson 2008; Feroz et al. 2009, 2013).”
The Radius of the High-mass Pulsar PSR J0740+6620 with 3.6 yr of NICER Data (2024, methodology): “We compute the posterior samples using PyMulti-Nest (Buchner et al. 2014) and MultiNest (Feroz & Hobson 2008; Feroz et al. 2009, 2019), as in the previous X-PSI analyses.”