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Importance Sampling - U-M LSA

Importance SamplingThe methods we ve introduced so far generate arbitrary points from a distribution to ap-proximate integrals in some cases many of these points correspond to points where thefunction value is very close to 0, and therefore contributes very little to the approxima-tion. In many cases the integral comes with a given density, such as integrals involvingcalculating an expectation. However, there will be cases where another distribution givesa better fit to integral you want to approximate, and results in a more accurate estimate; Importance Sampling is useful here.

This method is only considered reliable when the weights are not too variable. As a rule of thumb, when ESS = v u u t1 N XN i=1 w˜(X i) w −1 2 is less than 5, this method is reasonable. Here w is the sample mean of the ˜w(X i)’s. You will know you’ve chosen a bad g is ESS is large. When ESS < 5, the variance of E(h(X)) IS can be ...

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