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 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.

v1: 18 pages, 7 figures. v2: 22 pages, 9 figures: no changes to the algorithm, but more example distributions are provided against which the sampler is tested

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