Algorithm for the exact likelihood of a counting process

Abstract

The Poisson-gamma filter is a technique for updating estimates as new observations become available from a counting process model. It is shown that the Poisson-gamma filter could be used to calculate exact maximum likelihood estimates of the parameters in a counting process model. Adaptive estimation for a counting process model with non-linear intensity is a special case of this technique. Discrete-time models are obtained to handle unequally-spaced data.