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5 - Monte Carlo Sampling and Importance Sampling

Published online by Cambridge University Press:  27 July 2023

Daniel Sanz-Alonso
Affiliation:
University of Chicago
Andrew Stuart
Affiliation:
California Institute of Technology
Armeen Taeb
Affiliation:
University of Washington
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Summary

In this chapter we introduce Monte Carlo sampling and importance sampling. These are two general techniques for estimating expectations with respect to a given pdf π. Monte Carlo generates independent samples from π and combines them with equal weights, whilst importance sampling uses independent samples, weighted appropriately, from a different distribution. In quantifying the error in Monte Carlo and importance sampling, we will use a distance on random probability measures that reduces to total variation in the case of deterministic probability measures; and we will introduce the χ2 divergence.

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Publisher: Cambridge University Press
Print publication year: 2023

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