Multivariate hidden dynamic geostatistical model for analysing and mapping air quality data in Apulia, Italy

In this work we propose the multivariate extension of a spatio-temporal model known in the literature and we deduce its maximum likelihood estimator based on the EM algorithm. An illustrating example concerns the joint modeling of air quality and meteorology in Apulia region, Italy. In particular a 8-variate model is fitted for daily particulate matters (PM10) and nitrogen dioxides (NO2) concentrations and six non colocated meteorological variables, without the need of preliminary data interpolation. Some preliminary evidence of the model capability to detect a Saharan dust event is also given. We propose an extension of a univariate hierarchical model with a Markovian latent geostatistical component, which was introduced in the literature as the dynamic spatio-temporal model. Since it is given by a Markovian sequence of spatial random fields plus a measurement error, in this paper we refer to as the hidden dynamic geostatistical model, or HDG model. In the frame of large datasets, a semi-parametric variant of the HDG model was introduced as the fixed rank smoothing spatio-temporal random effect model (FRSSTRE). The univariate HDG has been addressed by both maximum likelihood and Bayesian techniques and some comparison studies showed its good performance in both cases. For estimation and prediction we develop an HDG extension of the D-STEM software which is able to handle multiple variables with heterogeneous spatial supports, covariates, heterotopic monitoring networks and missing data. Uncommon in the EM literature, also the standard deviation of parameter estimates are available. In the air quality example, concentration maps and the related uncertainty maps are estimated in order to highlight the potentiality and usefulness of the proposed approach in the context of official environmental communication.