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)
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)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6921d747-780d-47da-8f35-bd3246ee1611%2Ff173c44c-c8a0-4694-bb13-a70cb1618388%2F3xrn2xs_processed.jpeg&w=3840&q=75)
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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