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Activity Number: 455
Type: Topic Contributed
Date/Time: Wednesday, August 5, 2009 : 10:30 AM to 12:20 PM
Sponsor: Section on Bayesian Statistical Science
Abstract - #304575
Title: An Improved Analysis of the Product Estimator
Author(s): Mark Huber*+ and Sarah Schott
Companies: Duke University and Duke University
Address: Box 90320, Durham, NC, 27708-0320,
Keywords: Monte Carlo ; product estimator

Consider the classic problem of estimating the size of a set A by generating multiple iid variates from A and counting the number that fall in a small subset B. The number of samples needed to obtain guaranteed relative accuracy in the estimate is the measure of A divided by the measure of B. In many cases this is too small, therefore the product estimator was introduced, which works by introducing a series of nested sets A_1, A_2,... interpolating smoothly from B to A. For each, the measure of A_{i+1} divided by measure of A_i is estimated, and then the product of these estimates are used to estimate measure of A divided by measure of B. The variance of this product estimator is relatively simple to analyze, but bounding the tails requires more care. In this talk, a new method for analysis will be presented, improving the running time of all product estimators by a constant factor.

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