Sensitivity analysis via likelihood ratios
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TL;DR
It is proven that the method works for a wide class of parameters and performance measures in regenerative simulation and on the method's limitations and on some numerical experiments.
Abstract
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, NT is the number of Poisson events in (0, T),and ψ is nearly any function of the sample path (e.g. a performance measure in a queuing network), then we show that d/dλ Eλ(ψ) = Eλ ((NT/λ - T)ψ), 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.