Adaptive Independent Sticky MCMC algorithms

TL;DR

This paper introduces adaptive independent sticky MCMC algorithms that use iterative, non-parametric proposals to efficiently sample from complex target distributions, with proven convergence and practical extensions to multivariate cases.

Contribution

The paper presents a new class of adaptive MCMC algorithms employing non-parametric proposals built via interpolation, improving sampling efficiency and convergence control.

Findings

Algorithms effectively sample from complex univariate distributions.

Proposed methods extend to multivariate distributions within Gibbs sampling.

Numerical examples demonstrate superior efficiency over traditional methods.

Abstract

In this work, we introduce a novel class of adaptive Monte Carlo methods, called adaptive independent sticky MCMC algorithms, for efficient sampling from a generic target probability density function (pdf). The new class of algorithms employs adaptive non-parametric proposal densities which become closer and closer to the target as the number of iterations increases. The proposal pdf is built using interpolation procedures based on a set of support points which is constructed iteratively based on previously drawn samples. The algorithm's efficiency is ensured by a test that controls the evolution of the set of support points. This extra stage controls the computational cost and the convergence of the proposal density to the target. Each part of the novel family of algorithms is discussed and several examples are provided. Although the novel algorithms are presented for univariate target densities, we show that they can be easily extended to the multivariate context within a Gibbs-type sampler. The ergodicity is ensured and discussed. Exhaustive numerical examples illustrate the efficiency of sticky schemes, both as a stand-alone methods to sample from complicated one-dimensional pdfs and within Gibbs in order to draw from multi-dimensional target distributions.