Sensitivity analysis via likelihood ratios
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We present a new method of obtaining derivatives of expectations with respect to various parameters. For example, if λ is the rate of a Poisson process, <italic>N<subscrpt>T</subscrpt></italic> is the number of Poisson events in (0, <italic>T</italic>),and <italic>&psgr;</italic> is nearly any function of the sample path (e.g. a performance measure in a queuing network), then we show that <italic>d</italic>/<italic>d</italic>λ <italic>E</italic><subscrpt>λ</subscrpt>(&psgr;) = <italic>E</italic>λ ((<italic>N<subscrpt>T</subscrpt></italic>/λ - <italic>T</italic>)&psgr;), which yields an obvious algorithm. We have proven that the method works for a wide class of parameters and performance measures in regenerative simulation. We also report on the method's limitations and on some numerical experiments.
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