Modelling bedload transport events using an inhomogeneous gamma process

Abstract

Monitored sequences of bedload transport events in two small gravel-bedded trout streams are described. To model the event timings, the inhomogeneous gamma process, with the special case of the Poisson process, are introduced, in which the baseline intensity is related to a linear regression combination of covariates. These may be time-varying covariates, such as seasonal cycles, covariates specific to an individual process or covariates common to more than one process. It is shown that the maximum likelihood estimates of the regression parameters may be obtained by an iterative least-squares procedure. The procedure is demonstrated by application to the bedload transport event sequences.