Monte Carlo sampling for stochastic weight functions

TL;DR

This paper introduces a rigorous Monte Carlo algorithm that effectively handles fluctuating weight functions, enabling accurate sampling in noisy or high-throughput scenarios where weights are uncertain.

Contribution

It presents a novel Monte Carlo method for sampling with fluctuating weights, extending traditional algorithms to noisy and high-throughput data contexts.

Findings

The algorithm accurately samples points proportional to their average weight.

It can be applied to noisy datasets and high-throughput experiments.

The method improves robustness in stochastic weight scenarios.

Abstract

Conventional Monte Carlo simulations are stochastic in the sense that the acceptance of a trial move is decided by comparing a computed acceptance probability with a random number, uniformly distributed between 0 and 1. Here we consider the case that the weight determining the acceptance probability itself is fluctuating. This situation is common in many numerical studies. We show that it is possible to construct a rigorous Monte Carlo algorithm that visits points in state space with a probability proportional to their average weight. The same approach has the potential to transform the methodology of a certain class of high-throughput experiments or the analysis of noisy datasets.