Statistica Sinica 10(2000), 971-987

BAYESIAN VARIABLE SELECTION FOR TIME SERIES

COUNT DATA

Joseph G. Ibrahim$^{*\dagger}$, Ming-Hui Chen$^\char93$ and Louise M. Ryan$^{*\dagger}$

$^*$Harvard School of Public Health, $^\dagger$Dana-Farber Cancer

Institute and $^\char93$Worcester Polytechnic Institute

Abstract: We consider a parametric model for time series of counts by constructing a likelihood-based generalization of a model considered by Zeger (1988). We consider a Bayesian approach and propose a class of informative prior distributions for the model parameters that are useful for variable subset selection. The prior specification is motivated from the notion of the existence of data from similar previous studies, called historical data, which is then quantified in a prior distribution for the current study. We derive theoretical and computational properties of the proposed priors and develop novel methods for computing posterior model probabilities. To compute the posterior model probabilities, we show that only posterior samples from the full model are needed to estimate the posterior probabilities for all of the possible subset models. We demonstrate our methodology with a simulated and a real data set.

Key words and phrases: Correlated counts, Gibbs sampling, hierarchical centering, historical data, Poisson regression, posterior distribution.