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

The links between the likelihood-ratio (LR) gradient-estimation technique (sometimes called the score-function (SF) method), and infinitesimal perturbation analysis (IPA) are studied. It is shown how IPA can be viewed as a (degenerate) special case of the LR and SF techniques by selecting an appropriate representation of the underlying sample space for a given simulation experiment. It is also shown how different definitions of the sample space yield different variants of the LR method, some of them mixing IPA with more straightforward LR. This is illustrated by many examples. Also given are sufficient conditions under which the gradient estimators are unbiased.