SOME APPLICATIONS OF COUNTING PROCESS MODELS WITH PARTIALLY OBSERVED COVARIATES

A broad array of data series have embedded discrete event-occurrences. cumulative counts of which can be viewed as superpositions N(t) = Sig ma(i=1)(n) Ni(t) Of independent identically distributed (iid) counting processes with intensities of the form lambda(i)(t) = h(Z(i), V(t), V ), where V is unknown, n may be unknown, Z(i) are unobservable iid vec tors, and V(t) is an observable ''environmental'' vector process, but the function h is known or hypothesized. It is shown how such data-str uctures and models arise naturally within the application areas of env ironmental epidemiology and software reliability, and lead to statisti cal analyses using novel forms of Poisson regression models with rando m effects. Such models are potentially very useful in analysis and cha racterization of teletraffic patterns.