importance sampling

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A method of reducing the variance of an estimate obtained via simulation. Suppose, for example, that we wish to estimate the quantity I, given by , where g is a given function. An obvious method is to generate uniform pseudo-random numbers u1, u2,…, un, in the interval (0, 1). Writing u1, u2,…, un for the corresponding random variables, the estimator, I1, is . Importance sampling makes a more representative choice of values: suppose that f is a probability density function that resembles g in its general shape, and let F be the corresponding distribution function. Instead of working with u1, u2,…, un, we work with ν1, ν2,…, νn, where F(νj)=uj. The resulting estimator, I2, given by , will have a smaller variance than I1.

Subjects: Probability and Statistics.

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