Sampling using a ‘bank’ of clues

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 parameter 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.