A Sampling Strategy for High-Dimensional Spaces Applied to Free-Form Gravitational Lensing

TL;DR

This paper introduces a new sampling strategy for high-dimensional convex spaces, enhancing free-form gravitational lens modeling and applicable to other fields, by enabling efficient, uncorrelated sampling of complex parameter spaces.

Contribution

A novel proposal strategy for the Metropolis-Hastings algorithm that efficiently samples high-dimensional convex polytopes, improving gravitational lens reconstruction methods.

Findings

Successfully produces uniform uncorrelated samples

Improves exploration of degeneracies in lens modeling

Parallel implementation within GLASS framework

Abstract

We present a novel proposal strategy for the Metropolis-Hastings algorithm designed to efficiently sample general convex polytopes in 100 or more dimensions. This improves upon previous sampling strategies used for free-form reconstruction of gravitational lenses, but is general enough to be applied to other fields. We have written a parallel implementation within the lens modeling framework GLASS. Testing shows that we are able to produce uniform uncorrelated random samples which are necessary for exploring the degeneracies inherent in lens reconstruction.