Determining Frequentist Confidence Limits Using a Directed Parameter Space Search

TL;DR

This paper introduces a machine learning-based method for efficiently determining Frequentist confidence limits in high-dimensional, computationally expensive likelihood spaces, outperforming traditional MCMC in robustness and accuracy.

Contribution

A novel machine learning algorithm that intelligently targets likelihood evaluations to accurately map confidence regions in complex parameter spaces.

Findings

Accurately identifies high-likelihood regions in parameter space.

More robust against multi-modal likelihood functions than MCMC.

Efficiently characterizes likelihood surfaces in both low- and high-likelihood regions.

Abstract

We consider the problem of inferring constraints on a high-dimensional parameter space with a computationally expensive likelihood function. We propose a machine learning algorithm that maps out the Frequentist confidence limit on parameter space by intelligently targeting likelihood evaluations so as to quickly and accurately characterize the likelihood surface in both low- and high-likelihood regions. We compare our algorithm to Bayesian credible limits derived by the well-tested Markov Chain Monte Carlo (MCMC) algorithm using both multi-modal toy likelihood functions and the 7-year WMAP cosmic microwave background likelihood function. We find that our algorithm correctly identifies the location, general size, and general shape of high-likelihood regions in parameter space while being more robust against multi-modality than MCMC.