Reducing Variance by Reweighting Samples
Résumé
We devise methods of variance reduction for the Monte Carlo estimation of an expectation of the type E [φ(X, Y)], when the distribution of X is exactly known. The key general idea is to give each individual of a sample a weight, so that the resulting weighted empirical distribution has a marginal with respect to the variable X as close as possible to its target. We prove several theoretical results on the method, identifying settings where the variance reduction is guaranteed. We perform numerical tests comparing the methods and demonstrating their efficiency.
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