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Random variate generation/Importance sampling using integral transforms\ | |
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StyleBox["Eugene d\[CloseCurlyQuote]Eon\nNVIDIA", | |
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StyleBox["Wellington, New Zealand\nApril 5, 2020 (updated May 10, 2020)", | |
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We discuss various analytic and exact methods for deriving \ | |
importance-sampling procedures for 1D distributions f(r) on the half line r \ | |
\[Element] [0,\[Infinity]). Specifically:\ | |
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Sampling as a superposition of exponentials using the inverse Laplace \ | |
transform\ | |
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"Simulating the linear transport of light or particles often involves \ | |
drawing random variates from some given distribution on the half line, such \ | |
as free-path length sampling in homogeneous classical media where we draw \ | |
samples from the collision-rate density ", | |
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There are times where we wish to sample other distributions f(r) on the half \ | |
line where the CDF inversion method is not possible analytically. For \ | |
example, in non-classical transport where free-path lengths between collision \ | |
are not exponentially-distributed, we need sampling procedures for a large \ | |
class of distributions that give the chord-lengths in a given class of random \ | |
microstructure.\ | |
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"In this paper we discuss methods for sampling from a 1D distribution f(r) \ | |
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We find the exponential, which we know how to sample. Therefore, Erlang-2 \ | |
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We check to see we can sample inverse mfp s from w(s). The CDF of the weight \ | |
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