Markov process modelling and analysis of discrete data

Abstract

It is shown that any discrete probability distribution with non-negative support can be represented as a generalized Poisson process with state-dependent rates. By looking at empirical estimates of these rate parameters from data, models can be built in terms of an appropriate functional form for the rates of such an underlying generalized Poisson process. The dependence of these rates on the state of the process may offer insights into the mechanisms that generated the data. These ideas are illustrated with reference to two large data sets that have been compiled to be representative of control populations in animal toxicology, and in mutation research. © 1998 John Wiley & Sons, Ltd.