Riemann Sums for MCMC Estimation and Convergence Monitoring.

This paper develops an extension of the Riemann sum techniques of Philippe (1997b) in the setup of MCMCC algorithms. It shows that the technique applies equally well to the output of these algorithms, with similar speeds of convergence which improve upon the regular estimator. The restriction on the dimension associated with Riemann sums can furthermore be overcome by Rao-Blackwellization methods. This approach can also be used as a control variate technique in convergence assessment of MCMC algorithms by using genuine control variate, that is, functions with know expectations, which are available in full generality for constants and scores.