Multimodal nested sampling: an efficient and robust alternative to Markov Chain Monte Carlo methods for astronomical data analyses

By Farhan Feroz, M. Hobson. 2007

1,086 citations recorded by the source corpus.

In performing a Bayesian analysis of astronomical data, two difficult problems often emerge. First, in estimating the parameters of some model for the data, the resulting posterior distribution may be multimodal or exhibit pronounced (curving) degeneracies, which can cause problems for traditional Markov Chain Monte Carlo (MCMC) sampling methods. Secondly, in selecting between a set of competing models, calculation of the Bayesian evidence for each model is computationally expensive using existing methods such as thermodynamic integration. The nested sampling method introduced by Skilling, has greatly reduced the computational expense of calculating evidence and also produces posterior inferences as a by-product. This method has been applied successfully in cosmological applications by Mukherjee, Parkinson & Liddle, but their implementation was efficient only for unimodal distributions without pronounced degeneracies. Shaw, Bridges & Hobson recently introduced a clustered nested sampling method which is significantly more efficient in sampling from multimodal posteriors and also determines the expectation and variance of the final evidence from a single run of the algorithm, hence providing a further increase in efficiency. In this paper, we build on the work of Shaw et al. and present three new methods for sampling and evidence evaluation from distributions that may contain multiple modes and significant degeneracies in very high dimensions; we also present an even more efficient technique for estimating the uncertainty on the evaluated evidence. These methods lead to a further substantial improvement in sampling efficiency and robustness, and are applied to two toy problems to demonstrate the accuracy and economy of the evidence calculation and parameter estimation. Finally, we discuss the use of these methods in performing Bayesian object detection in astronomical data sets, and show that they significantly outperform existing MCMC techniques. An implementation of our methods will be publicly released shortly.

Subfields: Artificial Intelligence, Astronomy and Astrophysics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/efd9d0f337d809bfc718a7569f47a0c296afadbb

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Astronomy and Astrophysics

In Statistics and Probability

Citations in the corpus

Detection of a dark substructure through gravitational imaging (2009, methodology): “In our analysis, we replace the standard Nested Sampling used in Vegetti & Koopmans (2009a) with MULTINEST, a multimodal nested sampling algorithm developed by Feroz & Hobson (2008).”
Equation of state sensitivities when inferring neutron star and dense matter properties (2018, methodology): “For each scenario described in the previous section we obtain from MULTINEST a set of equally weighted posterior samples.”
A NICER View of PSR J0030+0451: Millisecond Pulsar Parameter Estimation (2019, methodology): “Nested sampling We implemented nested sampling using the open-source software MultiNest90 (Feroz & Hobson 2008; Feroz et al. 2009, 2013; Buchner et al. 2014).”
Constraining the Dense Matter Equation of State with Joint Analysis of NICER and LIGO/Virgo Measurements (2019, methodology): “We use the nested sampling software MultiNest to draw weighted samples from the posterior distribution of θ (Feroz & Hobson 2008; Feroz et al. 2009, 2013; Buchner et al. 2014).”
A NICER View of PSR J0030+0451: Implications for the Dense Matter Equation of State (2019, methodology): “Any mass–radius pair with a likelihood lower than this threshold will then be ignored in the nested sampling process by MULTINEST (see T. E. Riley & A. L. Watts 2019, in preparation, for a discussion on prior density implementation options for use with MULTINEST).”
polychord: nested sampling for cosmology (2015, methodology): “PolyChord at worst scales as NL ∼ O(D3), whereas MultiNest has an exponential scaling which emerges in higher dimensions.”
MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics (2008, background): “In our previous paper (Feroz & Hobson 2008– hereinafter FH08), we built on the work of Shaw et al. (2007) by pursuing further the notion of detecting and characterising multiple modes in the posterior from the distribution of nested samples, and presented a number of innovations that resulted in a…”
Neutrino non-standard interactions: A status report (2019, methodology): “We found the use of MULTINEST [252,253] to be particularly well suited to address all the aforementioned complications associated to this task.”
Two-dimensional kinematics of SLACS lenses – III. Mass structure and dynamics of early-type lens galaxies beyond z ≃ 0.1 (2011, methodology): “…expensive task of exploring the posterior distribution Pr(η | d) is accomplished by making use of the very efficient and robust MultiNest algorithm (Feroz & Hobson 2008; Feroz et al. 2009), which implements the ‘nested sampling’ Monte Carlo technique (Skilling 2004; Sivia & Skilling 2006), and…”
Bayesian inference for compact binary coalescences with bilby: validation and application to the first LIGO–Virgo gravitational-wave transient catalogue (2020, background): “The pymultinest sampler (Feroz & Hobson 2008; Feroz et al. 2009, 2013; Buchner et al. 2014) can implement periodic boundary conditions, but not reflective, which are treated as None.”
European Pulsar Timing Array Limits On An Isotropic Stochastic Gravitational-Wave Background (2015, methodology): “In Feroz & Hobson (2008) and Feroz, Hobson & Bridges (2009), this nested sampling framework was built upon with the introduction of the MULTINEST algorithm, which provides an efficient means of sampling from posteriors that may contain multiple modes and/or large (curving) degeneracies.”
Evidence for a maximum mass cut-off in the neutron star mass distribution and constraints on the equation of state (2017, methodology): “(9) using nested sampling with multinest (Feroz & Hobson 2008; Feroz et al. 2009; Buchner et al. 2014).”
Importance Nested Sampling and the MultiNest Algorithm (2013, methodology): “Our test problem here is the same one used in Allanach and Lester (2008); Feroz and Hobson (2008); Feroz et al. (2009).”
Inference of the cold dark matter substructure mass function at z = 0.2 using strong gravitational lenses (2014, methodology): “(11) The integral of equation (10) is calculated numerically with the MultiNest method by Feroz & Hobson (2008), which is based on the original nested sampling idea by Skilling (2004).”