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Importance Sampling, Sequential Importance Sampling and more.

Importance Sampling, Sequential Importance Sampling and more. CS-295 Spring 2008. Estimation. Function : An assignment of weights to a domain Summation Problems Ratio over sums. Example: Function over 3 variables. Specification: Function is a Product of smaller Functions.

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Importance Sampling, Sequential Importance Sampling and more.

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  1. Importance Sampling, Sequential Importance Sampling and more. CS-295 Spring 2008

  2. Estimation • Function : An assignment of weights to a domain • Summation Problems • Ratio over sums

  3. Example: Function over 3 variables

  4. Specification: Function is a Product of smaller Functions • X: A set over n variables • fi(y), i=1 to m is a function over a subset of X • f(X) is the product of all functions

  5. Distribution: A function whose weights sum to 1. Smoking lung Cancer Bronchitis X-ray Dyspnoea

  6. USE REJECTION SAMPLING

  7. f(X) g(x)

  8. Rejection Control • Given a constant c>0. • For j=1 to m • Accept x(j) with probability • r(j) = min {1,w(j)/c) • If x(j) is accepted update its weight as • w(*j)=w(j)/r(j) • Let g*(x) be the sampling distribution, then:

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