a Deeper Look into Importance Sampling

A Deeper Look into Importance Sampling - June 3, 2009

From last class, we have determined that an integral can be written in the form [math]\displaystyle{ I = \displaystyle\int h(x)f(x)\,dx }[/math] [math]\displaystyle{ = \displaystyle\int \frac{h(x)f(x)}{g(x)}g(x)\,dx }[/math] We continue our discussion of Importance Sampling here.

Importance Sampling

We can see that the integral [math]\displaystyle{ = \displaystyle\int \frac{h(x)f(x)}{g(x)}g(x)\,dx }[/math] is just [math]\displaystyle{ \displaystyle E_g(w(x)) \rightarrow }[/math]the expectation of w(x) with respect to g(x)