14:00 – 15:00 – Pierre Jacob (ESSEC Business School)
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, and how it helps in combining importance sampling and robust mean estimation techniques such as median-of-means.
Refreshments available between 15:00 – 15:30, Huxley Common Room (HXLY 549)