Nicola Branchini

In my PhD I work on developing new methodology and diagnostics for adaptive importance sampling, a class of methods to estimate expectations under complex distributions, such as those arising in Bayesian statistics, and rare event probability estimation. In particular, I have been focusing on the problem of distributions with intractable normalizing constants, which lead to biased estimators for which optimal importance sampling proposals are not well understood. Another challenging issue I worked on comes up when the distribution of interest has heavy tails with undefined moments, in which case many standard algorithms fail. Finally, I have recently started to work on diagnostics for IS, in particular tailored for the case when the distribution of interest has an intractable normalizing constant. All these project have natural applications in Bayesian statistics, probabilistic machine learning, but potentially beyond, as importance sampling is used in computational finance for estimating option prices or rare events estimation in, for example, complex climate models.