Monte Carlo Quasi-Heatbath by approximate inversion

TL;DR

This paper introduces a method to sample from a specific distribution using approximate solutions to linear systems, maintaining the correct distribution without requiring exact solutions.

Contribution

It presents a novel approach to preserve the target distribution while solving linear systems approximately, broadening the applicability of heatbath algorithms.

Findings

Allows sampling with low-accuracy linear solves

Generalizes to other distributions and systems

Maintains correct distribution despite approximation

Abstract

When sampling the distribution P(phi) ~ exp(-|A phi|^2), a global heatbath normally proceeds by solving the linear system A phi = eta, where eta is a normal Gaussian vector, exactly. This paper shows how to preserve the distribution P(phi) while solving the linear system with arbitrarily low accuracy. Generalizations are presented.