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Self-normalized importance sampling

For an unnormalized target density, self-normalized importance sampling uses weights

w_{i} = f (Y_{i}) / h (Y_{i})

and estimates expectations by

\sum_{i} w_{i} g (Y_{i}) / \sum_{i} w_{i}

. Resampling a point

Y_{i}

with probability proportional to

w_{i}

produces the associated weighted empirical distribution.

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