Transcription of Importance Sampling - Statistics
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Importance Sampling - Statistics
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. In other cases, such as when you want to evaluateE(X) where you can t even generate from the distribution ofX, Importance samplingis necessary.
Importance Sampling The methods we’ve introduced so far generate arbitrary points from a distribution to ap- ... 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
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