Monte Carlo sampling for stochastic weight functions
This incremental work addresses a common issue in numerical studies, potentially improving methods for high-throughput experiments or noisy data analysis.
The authors tackled the problem of Monte Carlo simulations with fluctuating weight functions, showing that a rigorous algorithm can sample states proportionally to their average weight.
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.