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Abstract:
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Recurrent events occur in a variety of scientific areas, so probabilistic models for their occurrence and inference methods for model parameters are important. For a unit denote by {N(s): s > 0} the stochastic process counting number of event occurrences on or before time s. Given an unobserved frailty Z and the history F(s-) just before time s, we study the class of models specified by the intensity process P{dN(s)=1|Z,F(s-)} = ZY(s)exp{Q(s,N(s-);a)+R(s;b)}l(E(s))ds, where Y(s) indicates that unit is still under study; Q and R are bounded predictable processes, E(s) is an observable predictable process with piecewise monotone increasing and differentiable paths; l(.) is a hazard rate function; and Z has some distribution H(.;e). Model parameters are l(.), a, b, and e. Recent inference methods for this class of models, which subsumes many existing models, will be presented.
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