Title: Weighted batch means estimators in Markov chain Monte Carlo,
Abstract: This paper proposes a family of weighted batch means variance estimators,
which are computationally efficient and can be conveniently applied in
practice. The focus is on Markov chain Monte Carlo simulations and estimation
of the asymptotic covariance matrix in the Markov chain central limit theorem,
where conditions ensuring strong consistency are provided. Finite sample
performance is evaluated through auto-regressive, Bayesian spatial-temporal,
and Bayesian logistic regression examples, where the new estimators show
significant computational gains with a minor sacrifice in variance compared
with existing methods.