Likelihood ratio derivative estimation for finite-time performance measures in generalized semi-Markov processes

Article Abstract:

The likelihood ratio derivative estimation for finite-time performance measures was examined using generalized semi-Markov processes (GSMP). The conditions that were developed for the applicability of this method primarily introduced constraints on the basic building blocks of the GSMP, which include the transition probabilities, the distribution and density functions of the event lifetimes, and the initial distribution. These compares to the conditions for infinitesimal perturbation analysis (IPA), which focus on the underlying structure of the GSMP. Examples of substantial classes of stochastic models for which the validity of the likelihood ratio method can be proven were provided. The GSMP conditions were validated in several practical contexts, specifically for large classes of queueing and reliability models.

Simulation methods, Simulation, Markov processes, Ratio and proportion, Ratios

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On the interchange of derivative and expectation for likelihood ratio derivative estimators

Article Abstract:

The work of L'Ecuyer (1990) on the validity of interchange between derivative and expectation is revisited. In the follow-up analysis, new insights into the conditions for the unbiasedness of the likelihood ratio derivative estimators are discussed. It also presents specific variants of the conditions which are easier to verify in practice. In addition, sufficient conditions that allow the derivative estimator to have finite moments up to a given order are proposed. Examples are given to illustrate these conditions, including an example of an unbiased derivative estimator which meets the conditions even though its variance is infinite. Finally, efforts are made to improve the first two examples presented in L'Ecuyer's 1990 analysis.

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A unified view of the IPA, SF, and LR gradient estimation techniques

Article Abstract:

There is a strong relationship between infinitesimal perturbation analysis (IPA) and the likelihood-ratio (LR) gradient-estimation technique, also known as the score-function (SF) method. IPA can be seen as a special case of the LR and SF methods by choosing an appropriate representation of the sample space for a particular simulation study. LR can be implemented in several different ways, and several properties of IPA can apply to LR. IPA and pure SF techniques can be combined and applied to an M/M/1 queue, but IPA is usually the most efficient technique.

Methods, Models, Transformations (Mathematics), Perturbation (Mathematics)

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