Importance sampling: Difference between revisions

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The basic idea of importance sampling is to sample the states from a different distribution to lower the variance of the estimation of '''E'''[''X;P''], or when sampling from ''P'' is difficult.

This is accomplished by first choosing a random variable <math>L\geq 0</math> such that '''E'''[''L'';''P'']&nbsp;=&nbsp;1 and that ''P''-[[almost everywhere]] <math>L(\omega)\neq 0</math>.

With the variatevariable ''L'' we define a probability <math>P^{(L)}</math> that satisfies

: <math>

\mathbf{E}[X;P] = \mathbf{E}\left[\frac{X}{L};P^{(L)}\right].