Graphical model selection for air quality time series

We propose an objective Bayes approach based on graphical models for learning dependencies among multiple air quality time series within the framework of Vector Autoregressive (VAR) models. Using a fractional Bayes factor approach, we obtain the marginal likelihood in closed form and construct an MCMC algorithm for Bayesian graphical model determination with limited computational burden. We apply our method to study the interactions between four air pollutants over the municipality of Milan (Italy).