Efficient Multivariate Initial Sequence Estimators for MCMC

TL;DR

This paper introduces an efficient multivariate initial sequence estimator for MCMC error assessment that maintains superior finite-sample performance and is computationally faster, with demonstrated effectiveness in various MCMC scenarios.

Contribution

The paper proposes a computationally efficient multivariate initial sequence estimator that retains the desirable properties of existing methods, improving practical applicability.

Findings

The new estimator is faster than traditional multivariate initial sequence estimators.

It maintains asymptotic properties and finite-sample performance.

Effectiveness is demonstrated through MCMC examples.

Abstract

Estimating Monte Carlo error is critical to valid simulation results in Markov chain Monte Carlo (MCMC) and initial sequence estimators were one of the first methods introduced for this. Over the last few years, focus has been on multivariate assessment of simulation error, and many multivariate generalizations of univariate methods have been developed. The multivariate initial sequence estimator is known to exhibit superior finite-sample performance compared to its competitors. However, the multivariate initial sequence estimator can be prohibitively slow, limiting its widespread use. We provide an efficient alternative to the multivariate initial sequence estimator that inherits both its asymptotic properties as well as the finite-sample superior performance. The effectiveness of the proposed estimator is shown via some MCMC example implementations. Further, we also present univariate and multivariate initial sequence estimators for when parallel MCMC chains are run and demonstrate their effectiveness over a popular alternative.