Kalman Filter for a Poisson Series with Covariates and Laplace Approximation Integration.

摘要

A hierarchical model for a Poisson time series is introduced. The model allows the mean or rate of the Poisson variables to vary slowly in time; it is modeled as the exponential of an AR/1 process. In addition the rate is influenced by a covariate. The Laplace method is used to recursively update some model parameter estimates. Frankly heuristic methods are explored to estimate other of the underlying parameters. The methodology is checked against simulated data with encouraging results.