Data extracted from air quality monitoring can require spatiotemporal clustering techniques. Of late, many clustering techniques are based on mixture models; however, there is a shortage of model‐based approaches for spatiotemporal data. A new mixture to cluster spatiotemporal data, named STM, is introduced, and generic identifiability is proved. The resulting model defines each mixture component as a mixture of autoregressive polynomial regressions in which the weights consider the spatial and temporal information with logistic links. Under the maximum likelihood framework, parameter estimation is carried out via an expectation–maximization algorithm while classical information criteria can be used for model selection. The proposed model is applied to air quality monitoring data from the periphery of Paris considering one of the critical pollutants, nitrogen dioxide, at different times during the day. The STM model is implemented in the R package SpaTimeClust.

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The receiver operating characteristic curve is widely applied in measuring the performance of diagnostic tests. Many direct and indirect approaches have been proposed for modelling the ROC curve, and because of its tractability, the Gaussian distribution has typically been used to model both populations. We propose using a Gaussian mixture model, leading to a more flexible approach that better accounts for atypical data. Monte Carlo simulation is used to circumvent the issue of absence of a closed-form. We show that our method performs favourably when compared to the crude binormal curve and to the semi-parametric frequentist binormal ROC using the famous LABROC procedure.