Bandwidth Selection for Kernel Density Estimation with a Markov Chain Monte Carlo Sample

TL;DR

This paper introduces new bandwidth selection methods for kernel density estimation tailored for dependent data from Markov Chain Monte Carlo samples, improving accuracy over standard techniques.

Contribution

The paper develops modified bandwidth selection criteria that account for dependence in MCMC samples, enhancing density estimation accuracy.

Findings

Proposed methods yield bandwidths near the optimal value.

Standard methods tend to undersmooth density estimates.

Proposed methods significantly reduce integrated mean squared error.

Abstract

Markov chain Monte Carlo samplers produce dependent streams of variates drawn from the limiting distribution of the Markov chain. With this as motivation, we introduce novel univariate kernel density estimators which are appropriate for the stationary sequences of dependent variates. We modify the asymptotic mean integrated squared error criterion to account for dependence and find that the modified criterion suggests data-driven adjustments to standard bandwidth selection methods. Simulation studies show that our proposed methods find bandwidths close to the optimal value while standard methods lead to smaller bandwidths and hence to undersmoothed density estimates. Empirically, the proposed methods have considerably smaller integrated mean squared error than do standard methods.