Diffusive Limits for Adaptive MCMC for Normal Target densities

TL;DR

This paper investigates the limiting behavior of an adaptive MCMC algorithm targeting a standard Normal distribution, demonstrating that its diffusion approximation converges to a standard Normal density.

Contribution

It applies diffusion approximation to adaptive MCMC for Normal targets, identifying the limiting distribution as standard Normal, which advances understanding of adaptive algorithms.

Findings

Diffusion limit is a standard Normal distribution.

The limiting process admits a density equal to the target.

Provides theoretical validation for adaptive MCMC convergence.

Abstract

In this paper we apply the Diffusion approximation procedure to a discrete time Adaptive Markov Chain Monte Carlo (AMCMC) method when the target distribution is standard Normal. We show that the limiting distribution of the diffusion admits a density which we identify as the standard Normal distribution.