Fully Adaptive Gaussian Mixture Metropolis-Hastings Algorithm

TL;DR

This paper introduces a fully adaptive Gaussian mixture Metropolis-Hastings algorithm that efficiently samples from complex multi-modal distributions by updating proposal parameters recursively, demonstrated through numerical experiments.

Contribution

The paper presents a novel adaptive Metropolis-Hastings method using Gaussian mixture proposals with recursive parameter updates for improved sampling efficiency.

Findings

Effective sampling from multi-modal distributions

Recursive parameter updates enhance convergence

Numerical results validate the method's performance

Abstract

Markov Chain Monte Carlo methods are widely used in signal processing and communications for statistical inference and stochastic optimization. In this work, we introduce an efficient adaptive Metropolis-Hastings algorithm to draw samples from generic multi-modal and multi-dimensional target distributions. The proposal density is a mixture of Gaussian densities with all parameters (weights, mean vectors and covariance matrices) updated using all the previously generated samples applying simple recursive rules. Numerical results for the one and two-dimensional cases are provided.