MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics

TL;DR

MultiNest presents a robust, parallelized ellipsoidal nested sampling framework to efficiently compute Bayesian evidence and sample posteriors that are multimodal or feature pronounced degeneracies. It introduces an EM-based partitioning of the active point set into overlapping ellipsoids within a unit hypercube, enabling automatic mode detection and local evidence evaluation. Through toy problems and cosmological data analyses, MultiNest demonstrates significantly reduced likelihood evaluations and reliable model selection versus traditional MCMC approaches, while providing accurate posterior constraints. The work also offers practical guidance for parameter settings and provides public availability, enhancing Bayesian inference in cosmology and particle physics contexts.

Abstract

We present further development and the first public release of our multimodal nested sampling algorithm, called MultiNest. This Bayesian inference tool calculates the evidence, with an associated error estimate, and produces posterior samples from distributions that may contain multiple modes and pronounced (curving) degeneracies in high dimensions. The developments presented here lead to further substantial improvements in sampling efficiency and robustness, as compared to the original algorithm presented in Feroz & Hobson (2008), which itself significantly outperformed existing MCMC techniques in a wide range of astrophysical inference problems. The accuracy and economy of the MultiNest algorithm is demonstrated by application to two toy problems and to a cosmological inference problem focussing on the extension of the vanilla $Λ$CDM model to include spatial curvature and a varying equation of state for dark energy. The MultiNest software, which is fully parallelized using MPI and includes an interface to CosmoMC, is available at http://www.mrao.cam.ac.uk/software/multinest/. It will also be released as part of the SuperBayeS package, for the analysis of supersymmetric theories of particle physics, at http://www.superbayes.org

Figures (9)

• Figure 1: Cartoon illustrating (a) the posterior of a two dimensional problem; and (b) the transformed $\mathcal{L}(X)$ function where the prior volumes $X_{i}$ are associated with each likelihood $\mathcal{L}_{i}$.
• Figure 2: Cartoon of ellipsoidal nested sampling from a simple bimodal distribution. In (a) we see that the ellipsoid represents a good bound to the active region. In (b)-(d), as we nest inward we can see that the acceptance rate will rapidly decrease as the bound steadily worsens. Figure (e) illustrates the increase in efficiency obtained by sampling from each clustered region separately.
• Figure 3: Illustrations of the ellipsoidal decompositions returned by Algorithm \ref{['alg:dino']}: the points given as input are overlaid on the resulting ellipsoids. 1000 points were sampled uniformly from: (a) two non-intersecting ellipsoids; and (b) a torus.
• Figure 4: Cartoon illustrating the assignment of points to groups; see text for details. The iso-likelihood contours $\mathcal{L}=\mathcal{L}_{i_1}$ and $\mathcal{L}=\mathcal{L}_{i_2}$ are shown as the dashed lines and dotted lines respectively. The solid circles denote active points at the nested sampling iteration $i=i_2$, and the open circles are the inactive points at this stage.
• Figure 5: Toy model 1: (a) two-dimensional plot of the likelihood function defined in Eq. \ref{['eq:eggbox']}; (b) dots denoting the points with the lowest likelihood at successive iterations of the MultiNest algorithm. Different colours denote points assigned to different isolated modes as the algorithm progresses.