Properties of the Affine Invariant Ensemble Sampler in high dimensions

TL;DR

This paper investigates the limitations of the affine-invariant ensemble sampler in high-dimensional settings, revealing that it exhibits undesirable properties and may produce inaccurate estimates as dimensionality increases.

Contribution

The paper provides a theoretical analysis of the affine-invariant ensemble sampler's behavior in high dimensions and highlights potential pitfalls for practitioners.

Findings

Short burn-in period observed in high dimensions

Mean and variance estimates deviate from true values as n increases

The sampler's performance deteriorates with increasing dimensionality

Abstract

We present theoretical and practical properties of the affine-invariant ensemble sampler Markov chain Monte Carlo method. In high dimensions the affine-invariant ensemble sampler shows unusual and undesirable properties. We demonstrate this with an $n$-dimensional correlated Gaussian toy problem with a known mean and covariance structure, and analyse the burn-in period. The burn-in period seems to be short, however upon closer inspection we discover the mean and the variance of the target distribution do not match the expected, known values. This problem becomes greater as $n$ increases. We therefore conclude that the affine-invariant ensemble sampler should be used with caution in high dimensional problems. We also present some theoretical results explaining this behaviour.