# Logarithmic Accuracy in Importance Sampling via Large Deviations

## TL;DR

This paper investigates the asymptotic behavior of importance sampling estimators for rare events using large deviations theory, offering new insights and diagnostics for their efficiency and sample size requirements.

## Contribution

It introduces a novel analysis of importance sampling estimators under non-optimal measures via large deviations, enhancing understanding of their asymptotic efficiency.

## Key findings

- Provides new theoretical insights into IS estimator behavior
- Proposes diagnostics for assessing IS efficiency
- Analyzes sample size requirements for rare event estimation

## Abstract

Importance sampling (IS) is a widely used simulation method for estimating rare event probabilities. In IS, the relative variance of an estimator is the most common measure of estimator accuracy, and the focus of existing literature is on constructing an importance measure under which the relative variance of the estimator grows sub-exponentially as the parameter increases. In practice, constructing such an estimator is not easy. In this work, we study the behavior of IS estimators under an importance measure which is not necessarily optimal using large deviations theory. This provides new insights into asymptotic efficiency of IS estimators and the required sample size. Based on the study, we also propose new diagnostics of IS for rare event simulation.