Ensemble Monte Carlo Calculations with Five Novel Moves

TL;DR

This paper enhances ensemble Monte Carlo methods by introducing five new move types, improving sampling efficiency and robustness, demonstrated through applications to complex high-dimensional densities.

Contribution

The paper presents five novel Monte Carlo moves, expanding the move set from three to eight, and adapts existing moves using simplex and directed strategies for better sampling.

Findings

Improved sampling efficiency on high-dimensional problems

Reduced autocorrelation times and travel times

Enhanced cohesion among walkers

Abstract

We introduce five novel types of Monte Carlo (MC) moves that brings the number of moves of ensemble MC calculations from three to eight. So far such calculations have relied on affine invariant stretch moves that were originally introduced by Christen (2007), 'walk' moves by Goodman and Weare (2010) and quadratic moves by Militzer (2023). Ensemble MC methods have been very popular because they harness information about the fitness landscape from a population of walkers rather than relying on expert knowledge. Here we modified the affine method and employed a simplex of points to set the stretch direction. We adopt the simplex concept to quadratic moves. We also generalize quadratic moves to arbitrary order. Finally, we introduce directed moves that employ the values of the probability density while all other types of moves rely solely on the location of the walkers. We apply all algorithms to the Rosenbrock density in 2 and 20 dimensions and to the ring potential in 12 and 24 dimensions. We evaluate their efficiency by comparing error bars, autocorrelation time, travel time, and the level of cohesion that measures whether any walkers were left behind. Our code is open source.