Challenges of Profile Likelihood Evaluation in Multi-Dimensional SUSY Scans

TL;DR

This paper evaluates the performance of MultiNest, a nested sampling algorithm, for profile likelihood analysis in supersymmetric models, revealing optimal configurations for accurate frequentist inference.

Contribution

It identifies a better MultiNest configuration for profile likelihood estimation, improving frequentist analysis in supersymmetric parameter space.

Findings

Standard MultiNest configuration poorly approximates profile likelihood.

A new configuration improves exploration and global maximum detection.

Properly configured MultiNest is suitable for profile likelihood studies.

Abstract

Statistical inference of the fundamental parameters of supersymmetric theories is a challenging and active endeavor. Several sophisticated algorithms have been employed to this end. While Markov-Chain Monte Carlo (MCMC) and nested sampling techniques are geared towards Bayesian inference, they have also been used to estimate frequentist confidence intervals based on the profile likelihood ratio. We investigate the performance and appropriate configuration of MultiNest, a nested sampling based algorithm, when used for profile likelihood-based analyses both on toy models and on the parameter space of the Constrained MSSM. We find that while the standard configuration is appropriate for an accurate reconstruction of the Bayesian posterior, the profile likelihood is poorly approximated. We identify a more appropriate MultiNest configuration for profile likelihood analyses, which gives an excellent exploration of the profile likelihood (albeit at a larger computational cost), including the identification of the global maximum likelihood value. We conclude that with the appropriate configuration MultiNest is a suitable tool for profile likelihood studies, indicating previous claims to the contrary are not well founded.