Markov Chain Monte Carlo Estimation of Quantiles

TL;DR

This paper develops methods for quantile estimation using Markov chain Monte Carlo, providing theoretical guarantees for the sampling distribution, variance estimation, and practical recommendations based on finite sample analysis.

Contribution

It introduces conditions for normality of Monte Carlo error, techniques for variance estimation, and evaluates finite sample properties for quantile estimation via MCMC.

Findings

Sampling distribution of Monte Carlo error is approximately Normal under certain conditions

Methods for estimating asymptotic variance are effective for interval construction

Finite sample analysis offers practical guidance for practitioners

Abstract

We consider quantile estimation using Markov chain Monte Carlo and establish conditions under which the sampling distribution of the Monte Carlo error is approximately Normal. Further, we investigate techniques to estimate the associated asymptotic variance, which enables construction of an asymptotically valid interval estimator. Finally, we explore the finite sample properties of these methods through examples and provide some recommendations to practitioners.