Squeezing. Let S and X have density functions satisfying b(x) ≤ fs(x) ≤ a(x) and fs(x) ≤ fx(x). Let U be uniformly distributed on [0, 1] and independent of X. Given the value X, we implement the following algorithm: if Ufx (X) > a(X), otherwise: if Ufx (X)

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Squeezing. Let S and X have density functions satisfying b(x) ≤ fs(x) ≤ a(x) and fs(x) ≤
fx(x). Let U be uniformly distributed on [0, 1] and independent of X. Given the value X, we
implement the following algorithm:
if Ufx (X) > a(X),
otherwise: if Ufx (X) <b(X),
otherwise: if Ufx (X) ≤ fs(X),
otherwise: reject X.
reject X;
accept X;
accept X;
Show that, conditional on ultimate acceptance, X is distributed as S. Explain when you might use this
method of sampling.
Transcribed Image Text:Squeezing. Let S and X have density functions satisfying b(x) ≤ fs(x) ≤ a(x) and fs(x) ≤ fx(x). Let U be uniformly distributed on [0, 1] and independent of X. Given the value X, we implement the following algorithm: if Ufx (X) > a(X), otherwise: if Ufx (X) <b(X), otherwise: if Ufx (X) ≤ fs(X), otherwise: reject X. reject X; accept X; accept X; Show that, conditional on ultimate acceptance, X is distributed as S. Explain when you might use this method of sampling.
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