Sampling using a `bank' of clues

TL;DR

This paper introduces a modified Metropolis Algorithm that efficiently samples multi-modal distributions in moderate dimensions by utilizing a 'bank' of prior samples, improving exploration in physics research.

Contribution

It presents a novel sampling method that leverages existing low-quality or uncertain information to enhance exploration of complex distributions in physics applications.

Findings

Effective in sampling multi-modal distributions

Utilizes prior 'bank' of points from previous work

Balances exploration without user intervention

Abstract

An easy-to-implement form of the Metropolis Algorithm is described which, unlike most standard techniques, is well suited to sampling from multi-modal distributions on spaces with moderate numbers of dimensions (order ten) in environments typical of investigations into current constraints on Beyond-the-Standard-Model physics. The sampling technique makes use of pre-existing information (which can safely be of low or uncertain quality) relating to the distribution from which it is desired to sample. This information should come in the form of a ``bank'' or ``cache'' of space points of which at least some may be expected to be near regions of interest in the desired distribution. In practical circumstances such ``banks of clues'' are easy to assemble from earlier work, aborted runs, discarded burn-in samples from failed sampling attempts, or from prior scouting investigations. The technique equilibrates between disconnected parts of the distribution without user input. The algorithm is not lead astray by ``bad'' clues, but there is no free lunch: performance gains will only be seen where clues are helpful.