a Deeper Look into Importance Sampling: Difference between revisions
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====Importance Sampling==== | ====Importance Sampling==== | ||
We can see that the integral is just <math>\displaystyle E_g(w(x)) \rightarrow</math>the expectation of w(x) with respect to g(x) | We can see that the integral <math>= \displaystyle\int \frac{h(x)f(x)}{g(x)}g(x)\,dx</math> is just <math>\displaystyle E_g(w(x)) \rightarrow</math>the expectation of w(x) with respect to g(x) | ||
====Jenson's Inequality==== | ====Jenson's Inequality==== | ||
===[[Continuing on]] - June 5, 2009=== | ===[[Continuing on]] - June 5, 2009=== | ||
Revision as of 21:24, 3 June 2009
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)