# ORIE Colloquium: Mark Huber M.S. '97, Ph.D. '99 (Claremont McKenna) - Adaptive Estimation for Monte Carlo Data

## Location

https://cornell.zoom.us/j/546984188
Techniques such as perfect simulation can give unbiased estimates for high-dimensional integrals of interest, but the errors in those integrals remain difficult to bound. Classical estimators for mean and standard deviation usually use a fixed number of samples, and usually, it is not possible to describe the relative error precisely with these estimates. \emph{Adaptive} estimators utilize a random number of samples in creating their estimate, and so are well suited for data coming from Monte Carlo simulations. In this talk, I will present a range of adaptive estimators that have guaranteed bounds on the relative error of the estimate. First, an adaptive estimate for estimating the mean $p$ of a $\{0, 1\}$ random variable where the relative error distribution is independent of $p$. Next, an adaptive extension of the Jerrum, Valiant, and Vazirani self-reducibility method where the result is a simple Poisson rather than the product of binomials. Third, an estimate for $[0, 1]$ random variables that matches the best running time possible to first order. Last, an estimate for random variables $X$ with $\mathbb{E}[X] \leq \alpha \mathsf{SD}(X)$ where $\alpha$ is known that is best possible up to first order.