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Title: Unbiased estimation for discretized models and its extension to underdamped langevin dynamics Authors:  Ajay Jasra - KAUST (Saudi Arabia) [presenting]
Abstract: The focus is on computing expectations w.r.t. probability measures which are subject to discretization error. Examples include partially observed diffusion processes or inverse problems, where one may have to discretize time and/or space, in order to work with the probability of interest practically. Given access only to these discretizations, we consider constructing the construction of unbiased Monte Carlo estimators of expectations w.r.t. such target probability distributions. It is shown how to obtain such estimators using a novel adaptation of randomization schemes and Markov simulation methods. Under appropriate assumptions, these estimators possess finite variance and finite expected cost. This approach has two important consequences:(i) unbiased inference is achieved at the canonical complexity rate, and (ii) the resulting estimators can be generated independently, thereby allowing strong scaling to arbitrarily many parallel processors. Several algorithms are presented and applied to Bayesian inverse problems. We also show how this framework can be extended to unbiased MCMC associated with underdamped Langevin dynamics.