Exploring phase space with Nested Sampling

TL;DR

This paper demonstrates the novel application of Nested Sampling to explore high-dimensional phase space in particle collision events, improving efficiency over traditional methods and opening new avenues for Bayesian inference in particle physics.

Contribution

It adapts Nested Sampling for particle physics, enabling efficient integration and event generation in high-dimensional phase space, outperforming traditional algorithms.

Findings

Nested Sampling outperforms Vegas in efficiency

Achieves results comparable to multi-channel importance sampling

Potential for combining with non-flat priors to reduce variance

Abstract

We present the first application of a Nested Sampling algorithm to explore the high-dimensional phase space of particle collision events. We describe the adaptation of the algorithm, designed to perform Bayesian inference computations, to the integration of partonic scattering cross sections and the generation of individual events distributed according to the corresponding squared matrix element. As a first concrete example we consider gluon scattering processes into 3-, 4- and 5-gluon final states and compare the performance with established sampling techniques. Starting from a flat prior distribution Nested Sampling outperforms the Vegas algorithm and achieves results comparable to a dedicated multi-channel importance sampler. We outline possible approaches to combine Nested Sampling with non-flat prior distributions to further reduce the variance of integral estimates and to increase unweighting efficiencies.