Batch Size Selection for Variance Estimators in MCMC

We consider batch size selection for a general class of multivariate means variance estimators, which are computationally viable high-dimensional Markov chain Monte Carlo simulations. derive the asymptotic mean squared error this estimators. Further, we propose parametric technique estimating optimal sizes and discuss practical issues regarding process. Vector auto-regressive, Bayesian logistic regression, dynamic space-time examples illustrate quality estimation procedure where proposed outperform current methods.