Speaker: Professor Francois Perron, University of Montreal
Abstract: In this talk we will give an introduction to the Metropolis-Hastings Independent Algorithm (MHIA) and we will see how this algorithm can be improved. Our first approach will use a control variate based on the sample generated by the proposal. We will derive the variance of our estimator for fixed sample sizes n and show that, as n tends to infinity, the variance of our estimator is asymptotically better than the one obtained with the MHIA . Our second approach will be based on Jensen's inequality. We will use a Rao-Blackwellisation and we will exploit the lack of symmetry in the MHIA. We will find and upper bound on the improvements that we can obtain by these methods.