The Webinar Committee of the International Indian Statistical Association (lISA) proudly presents a webinar on "MCMC Importance Sampling via Moreau-Yosida Envelopes".
08/27/2024 | 11:00 AM - 12:00 PM (Eastern) / 10:00 AM - 11:00 AM (Pacific)
Abstract: Markov chain Monte Carlo (MCMC) is the workhorse computational algorithm for inference in Bayesian statistics. Gradient-based MCMC algorithms are known to yield faster converging Markov chains. In modern parsimonious models, the use of non-differentiable priors is fairly standard, leading to non-differentiable posteriors. Without differentiability, gradient-based MCMC algorithms cannot be employed effectively. Recently proposed proximal MCMC approaches, however, can partially remedy this limitation. These approaches use the Moreau-Yosida (MY) envelope to smooth the non-differentiable prior, enabling sampling from an approximation to the target posterior. In this work, we leverage properties of the MY envelope to construct an importance sampling paradigm that corrects for this approximation error. We establish the asymptotic normality of the importance sampling estimators, providing an explicit expression for the asymptotic variance, which we use to derive a practical metric of sampling efficiency. Numerical studies show that the proposed scheme can yield lower variance estimators compared to existing proximal MCMC alternatives.
Speaker Bio: Dr. Dootika Vats is an Associate Professor in the Department of Mathematics and Statistics at the Indian Institute of Technology Kanpur. Previously, she was an NSF Postdoctoral Fellow with Prof. Gareth Roberts at the University of Warwick. She earned her PhD from the University of Minnesota, Twin Cities, working with Prof. Galin Jones, and she received her undergraduate degree in Mathematics from Lady Shri Ram College. Her research interests include Markov chain Monte Carlo, output analysis for stochastic simulation, and stochastic optimization. She serves as an Associate Editor for the Journal of Computational and Graphical Statistics and Sankhya B.
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Himel Mallick, PhD, FASA
Principal Investigator (Tenure-track Faculty)
Cornell University
New York, New York 10065
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