# Dane Johnson : Large deviations, moderate deviations, and importance sampling

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.

**Category**: Probability**Duration**: 01:34:47**Date**: January 28, 2016 at 4:25 PM**Views**: 115-
**Tags:**seminar, Probability Seminar

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