On the validity of the batch quantile method for Markov chains

The estimation of quantiles of the steady-state distribution of a (general state-space) Markov chain (MC) from observations (e.g., simulated) of the corresponding MC is an important problem. For example, this estimation is required when constructing prediction intervals for a response variable W = g(Q) and Markov chain Monte Carlo has been applied to obtain information on the posterior distribution p(Q|x) of Q (where x represents a vector of data). Recent results show that a batch quantile methodology (similar to the batch means method) can be applied to obtain confidence intervals that are asymptotically valid under the assumption that the MC is exponentially ergodic. In this symposium we are interested in theoretical and application results on the validity of the batch quantile method for Markov chains, empirical assessments on the assumptions that are necessary for the validity of the batch quantile method as well as successful applications of the batch quantile method in any areas are especially welcome.