aThe information content of multivariable spatio-temporal data depends on the underlying spatial sampling scheme. The most informative case is represented by the isotopic configuration where all variables are measured at all sites. The opposite case is the completely heterotopic case where different variables are observed only at different locations. A well known approach to multivariate spatio-temporal modelling is based on the linear coregionalization model (LCM).In this paper, the maximum likelihood estimation of the heterotopic spatio-temporal model with spatial LCM components and temporal dynamics is developed. In particular, the computation of the estimates is based on the EM algorithm and two solutions are proposed: one is based on the more cumbersome exact maximization of the a posteriori expected log likelihood and the other is an approximate closed-form solution. Their properties are assessed in terms of bias and efficiency through an example of air quality dinamic mapping using satellite data and a Monte Carlo simulation campaign based on a large data set.

This paper discusses the software D-STEM as a statistical tool for the analysis and mapping of environmental space-time variables. The software is based on a flexible hierarchical space-time model which is able to deal with multiple variables, heterogeneous spatial supports, heterogeneous sampling networks and missing data. Model estimation is based on the expectation maximization algorithm and it can be performed using a distributed computing environment to reduce computing time when dealing with large data sets. The estimated model is eventually used to dynamically map the variables over the geographic region of interest. Three examples of increasing complexity illustrate usage and capabilities of D-STEM, both in terms of modeling and implementation, starting from a univariate model and arriving at a multivariate data fusion with tapering.

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e Multivariate spatio-temporal statistical models are deserving for increasing attention for environmental data in general and for air quality data in particular because they can reveal dependencies and spatio-temporal dynamics across multiple variables and can be used to obtain dynamic concentration maps over specified areas. In this frame, we introduce a multivariate generalization of a known spatio-temporal model referred to as the hidden dynamic geostatistical model. Maximum likelihood parameter estimates are obtained implementing the expectation maximization algorithm and suitably extending the D-STEM software, recently introduced for alternative model specifications, allowing to handle multiple variables with heterogeneous spatial support, covariates, and missing data. A case study illustrates some of the statistical issues typical of a medium complexity problem related to air quality data modeling. Considering air quality and meteorological data over the Apulia region, Italy, the usual approach using meteorological variables as regressors is not possible because these data are observed on different monitoring networks, and preliminary spatial interpolation to co-locate the data is to be avoided. Hence, an eight-variate model is considered for understanding the relations between daily concentrations of particulate matters (PM 10 ) and nitrogen dioxides (NO 2 ) and six non co-located meteorological variables. Model interpretation is given, and its use for dynamic map construction, uncertainty included, is illustrated. Moreover, some preliminary evidence of the model capability to detect a Saharan dust event is presented.

The Earthquake Network research project implements a crowdsourced earthquake early warning system based on smartphones. Smartphones, which are made available by the global population, exploit the Internet connection to report a signal to a central server every time a vibration is detected by the on-board accelerometer sensor. This paper introduces a statistical approach for the detection of earthquakes from the data coming from the network of smartphones. The approach allows to handle a dynamic network in which the number of active nodes constantly changes and where nodes are heterogeneous in terms of sensor sensibility and transmission delay. Additionally, the approach allows to keep the probability of false alarm under control. The statistical approach is applied to the data collected by three subnetworks related to the cities of Santiago (Chile), Iquique (Chile) and Kathmandu (Nepal). The detection capabilities of the approach are discussed in terms of earthquake magnitude and detection delay. A simulation study is carried out in order to link the probability of detection and the detection delay to the behaviour of the network under an earthquake event.