Sampling using a `bank of clues

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.

💡 Research Summary

The paper introduces a practical variant of the Metropolis‑Hastings algorithm that is specially designed for sampling from multimodal probability distributions in moderate‑dimensional spaces (roughly ten dimensions), a situation frequently encountered in contemporary Beyond‑the‑Standard‑Model (BSM) physics studies. The core idea is to augment the usual local proposal mechanism with a “bank of clues” – a pre‑assembled collection of points that are believed, at least partially, to lie near regions of high posterior probability. These clues can be obtained from earlier exploratory runs, aborted chains, discarded burn‑in samples, or any other source of partial information, even if the quality of that information is uncertain.

Algorithmic structure.
At each iteration the sampler decides, with probability ε (typically 0.1–0.3), whether to generate a proposal from the traditional local kernel q₀ (e.g., a Gaussian centered on the current state) or to draw a candidate directly from the clue bank B = {b₁,…,b_N}. When a clue is chosen, it is selected according to a weight w_i that may reflect prior belief, previous posterior estimates, or simply be uniform. The forward proposal probability is therefore
 q(x→b_i) = ε·w_i,
while the reverse probability from the clue back to the current state is
 q(b_i→x) = (1−ε)·q₀(b_i→x).
The Metropolis‑Hastings acceptance ratio remains the standard
 α = min{1,