Bayesian variable selection for time series count data

We consider a parametric model for time series of counts by constructing a likelihood-based generalization of a model considered by Zeger (1988). We c onsider a Bayesian approach and propose a class of informative prior distri butions for the model parameters that are useful for variable subset select ion. The prior specification is motivated from the notion of the existence of data from similar previous studies, called historical data, which is the n quantified in a prior distribution for the current study. We derive theor etical and computational properties of the proposed priors and develop nove l methods for computing posterior model probabilities. To compute the poste rior model probabilities, me show that only posterior samples from the full model are needed to estimate the posterior probabilities for all of the po ssible subset models. We demonstrate our methodology with a simulated and a real data set.