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Zero-Variance Hamiltonian MCMC

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If you have a question about this talk, please contact Mustapha Amrani.

Advanced Monte Carlo Methods for Complex Inference Problems

Interest is in evaluating, by Markov chain Monte Carlo (MCMC) simulation, the expected value of a function with respect to a, possibly unnormalized, probability distribution. A general purpose variance reduction technique for the MCMC estimator, based on the zero-variance principle introduced in the physics literature, is proposed. The main idea is to construct control variates based on the score function. Conditions for asymptotic unbiasedness of the zero-variance estimator are derived. A central limit theorem is also proved under regularity conditions. The potential of the zero-variance strategy is illustrated with real applications to probit, logit and GARCH Bayesian models. The Zero-Variance principle is efficiently combined with Hamiltonian Monte Carlo and Metropolis adjusted Langevin algorithms without exceeding the computational requirements since its main ingredient (namely the score function) is exploited twice: once to guide the Markov chain towards relevant portion of the state space via a clever proposal, that exploits the geometry of the target and achieves convergence in fewer iterations, and then to post-process the simulated path of the chain to reduce the variance of the resulting estimators.

This talk is part of the Isaac Newton Institute Seminar Series series.

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