Probability Seminar
Thursday, January 28, 2016, 4:30pm, 119 Physics
Dane Johnson (UNC - Chapel Hill)
Large deviations, moderate deviations, and importance sampling
Abstract:
Importance sampling is an accelerated Monte Carlo algorithm that can reduce variance when estimating small probabilities. The design of the algorithm involves the choice of a change of measure, and based on this choice the performance can range from substantially better than standard Monte Carlo to substantially worse. One approach to choosing a change of measure involves embedding the problem of interest in a sequence of processes that satisfies a large deviations principle, and then basing the change of measure on subsolutions to the Hamilton-Jacobi-Bellman equation associated the large deviations rate function. This approach has the benefit of guaranteeing a certain level of asymptotic performance based on the subsolution, but different embeddings can lead to different rate functions, subsolutions, and consequently different algorithms. I will contrast the strengths and weaknesses of two different embeddings, one using a scaling commonly referred to as the standard large deviations scaling and the other using a scaling referred to as moderate deviations. [video]

Generated at 9:11pm Thursday, March 28, 2024 by Mcal.   Top * Reload * Login