Monte Carlo methods and zero variance principle

Abstract

The principle dates back to 1999, when it was introduced in the physics literature by [3]. The physical nomenclature would broadly describe ZV estimators as renormalized observables used in Monte Carlo simulation with the same mean and smaller variance than the original observables of interest. More than a decade later, [18] brought ZV to the attention of the statistical community. In statistically oriented terms, ZV is a variance reduction scheme for Markov Chain Monte Carlo (MCMC) algorithms based on a specific form of control variates.

Theodore Papamarkou

Professor in maths of data science

Knowing is not enough, one must compute.