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

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 $\Lambda$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

• The paper demonstrates that MultiNest significantly improves the efficiency of Bayesian inference by employing multimodal nested sampling over traditional MCMC methods.
• It uses an optimal ellipsoidal decomposition to reduce the sampling volume, achieving precise evidence estimates and effective mode identification.
• MultiNest leverages parallel MPI computing to expedite analysis in high-dimensional spaces, benefiting research in cosmology and particle physics.

Overview of MultiNest: An Efficient Bayesian Inference Tool

The paper presents significant advancements in the development of the MultiNest algorithm, a Bayesian inference tool designed for efficiently calculating the evidence and providing posterior samples, particularly for distributions characterized by multiple modes and intricate degeneracies in high-dimensional spaces. Initially, Bayesian inference divides into parameter estimation and model selection, traditionally implemented via Markov chain Monte Carlo (MCMC) sampling. However, MCMC methods often face challenges, particularly with multimodal posterior distributions or those with significant parameter degeneracies. MultiNest addresses these limitations by employing a nested sampling approach, enhancing both the efficiency and robustness of Bayesian inference computationally.

Key Contributions

The paper underscores several vital contributions regarding the MultiNest algorithm:

1. Enhanced Sampling Efficiency: The algorithm incorporates a multimodal nested sampling technique that not only calculates the Bayesian evidence with an associated error estimate but also efficiently samples posterior distributions with multiple modes and pronounced degeneracies. Compared to previous methods, it significantly improves sampling efficiency for complex distributions.
2. Ellipsoidal Nested Sampling: MultiNest advances upon the concept of ellipsoidal nested sampling by crafting an optimal ellipsoidal decomposition of parameter space for sampling. This method reduces the volume of parameter space required for sampling, therein leading to higher sampling efficiencies, particularly in high-dimensional contexts.
3. Parallelization: The algorithm fully leverages parallel computing with Message Passing Interface (MPI) to expedite processing time, thereby accommodating a larger number of active points, crucial for accurate multimodal exploration.
4. Mode Identification and Local Evidence Calculation: As part of its core methodology, MultiNest naturally identifies individual modes within a distribution and separately computes the 'local' evidence and constraints associated with each mode. This feature allows for precise and detailed model selection processes.

Practical and Theoretical Implications

The MultiNest algorithm is shown to distinctly outperform classical MCMC techniques, particularly in scenarios presenting complex inference challenges, such as those in cosmology and particle physics. The application's efficiency implies that it requires significantly fewer likelihood evaluations compared to traditional methods, making it a valuable tool for computational cosmology. Given its ability to handle multi-modal spaces adeptly and its open-source availability, researchers can employ MultiNest to explore broader and more complex datasets without the computational burdens typically associated with Bayesian inference.

MultiNest's implications extend beyond its immediate applications, potentially influencing future approaches in Bayesian computation, particularly as we move towards more nuanced models incorporating greater numbers of parameters. Its design also presents opportunities for further refinements and adaptations, particularly in addressing increasingly large-scale problems as computational power expands.

Speculative Future Developments

Anticipating future developments consequent to this research, MultiNest holds the promise of being foundational in refining cosmological models, including extending the vanilla ΛCDM model. Additionally, as more ambitious particle physics models emerge, necessitating rigorous parameter estimation and model comparison, MultiNest's efficient evidence computation and flexible sampling will likely catalyze new insights and facilitate discoveries otherwise stymied by computational constraints.

In conclusion, the MultiNest algorithm presented in this paper constitutes a significant improvement over traditional Bayesian inference methods, offering a robust framework that efficiently handles complex, high-dimensional, and multimodal datasets prevalent in advanced fields such as astrophysics and particle physics.