Archive : Probability

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Gabriel Stoltz: CERMICS, Ecole des Ponts & INRIA Paris93Gabriel Stoltz: CERMICS, Ecole des Ponts & INRIA ParisZoom<br> Title: Longtime convergence of some diffusion processes in molecular dynamics <br> Abstract: I will present an introduction to two paradigmatic diffusion processes in molecular simulation, namely Langevin dynamics and its overdamped limit. I will in particular present results on their longtime convergence, based on Poincare inequalities for overdamped Langevin dynamics, and hypocoercive techniques for Langevin dynamics. I will also discuss the implication of these results in terms of estimates on the asymptotic variance of longtime averages, a key elements to quantify the statistical error in numerical simulations.4/28/2021 5:00:00 PM4/28/2021 6:00:00 PM
Kevin K. Lin, University of Arizona94Kevin K. Lin, University of ArizonaZoom<br> Title: Couplings-based sensitivity estimates for stochastic dynamics <br> Abstract: A common task in computational studies of stochastic dynamical systems is to estimate local sensitivities, i.e., how (stationary) expectations of observables vary with model parameters. Sensitivity estimates can be computationally expensive, and numerical methods based on couplings are often used to speed up such computations. Unfortunately, the simplest such methods may be ineffective for chaotic dynamics. In this talk, I will report on a study of coupling-based sensitivity estimators applicable to chaotic systems, examine their performance under different dynamical scenarios, and (time permitting) discuss their use in analyzing the parameter dependence of stochastic dynamical systems. This is joint work with Jonathan Mattingly (Duke) and Andrew Leach (University of Arizona, now at Google). 4/21/2021 5:00:00 PM4/21/2021 6:00:00 PM
Robert Webber (Courant Inst., NYU)92Robert Webber (Courant Inst., NYU)Zoom<br> Title: A splitting method to reduce MCMC variance <br> Abstract: We explore whether splitting and killing methods can improve the accuracy of Markov chain Monte Carlo (MCMC) estimates of rare event probabilities, and we make three contributions. First, we prove that "weighted ensemble" is the only splitting and killing method that provides asymptotically consistent estimates when combined with MCMC. Second, we prove a lower bound on the asymptotic variance of weighted ensemble's estimates. Third, we give a constructive proof and numerical examples to show that weighted ensemble can approach this optimal variance bound, in many cases reducing the variance of MCMC estimates by multiple orders of magnitude.3/24/2021 5:00:00 PM3/24/2021 6:00:00 PM
Ross Pinsky (Technion)91Ross Pinsky (Technion)EWG 336Title: Natural Probabilistic Model on the Integers and its Relation to Dickman-Type Distributions and Buchstab’s Function <br><br> Abstract: <a href="https://www.mathsci.udel.edu/content-sub-site/Documents/dickman-buchstab-abstract.pdf">Click here to view the abstract</a> 2/17/2020 6:30:00 PM2/17/2020 7:30:00 PM

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