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The EM algorithm for air quality spatio-temporal models

In Fasso and Nicolis (2006), Fasso et al. (2005) and Fasso et al. (2007) it has been proposed a hierarchical model for air quality data collected by the heterogeneous network of the entire Po valley. Generalizing this approach, in Cameletti (2007) a one-dimensional hidden state hierarchical model has been proposed for modelling the relation between observed PM10 concentrations and emission inventory data; in particular, it considers a spatio-temporal structure and an improved parameter estimation based on the EM algorithm (McLachlan and Krishnan (1997), Xu and Wikle (2007)). In Fasso and Cameletti (2007) the previous model has been extended considering a p-dimensional latent variable. This paper, which refers to Fasso and Cameletti (2007) for the details and the notation, focuses on the estimation procedure using the EM algorithm.