UCPH Statistics Seminar: Pierre Jacob

Speaker: Pierre Jacob from ESSEC Business School, Paris

Title: Some new results on the bias of self-normalized importance sampling and independent Metropolis--Rosenbluth--Teller--Hastings

Abstract: Suppose that you can draw N variables from a probability distribution q, but that you are really interested in a probability distribution pi on the same space. You can evaluate the density of pi point-wise, up to a multiplicative constant. How can you select one of the N draws in such a way that the marginal distribution of the selected sample is close to pi, e.g. in total variation distance? Importance sampling and independent Metropolis--Rosenbluth--Teller--Hastings (IMRTH) provide two solutions, both using pointwise evaluations of the Radon--Nikodym derivative of the target distribution relative to the proposal, which is called the weight function.  Under the weak assumption that the weight is unbounded but has a number of finite moments under the proposal distribution, we obtain new results on the approximation error of importance sampling and of independent Metropolis--Hastings algorithm (IMRTH). To obtain these results we employ a common random numbers coupling that we show to be maximal. We further consider bias removal techniques for self-normalized importance sampling. This is joint work with George Deligiannidis (University of Oxford), El Mahdi Khribch (ESSEC Business School), and Guanyang Wang (Rutgers University).