Accounting for covariate information in the scale component of spatio-temporal mixing models

Spatio-temporal processes in the environmental science are usually assumed to follow a Gaussian process, possibly after some transformation. Gaussian processes might not be appropriate to handle the presence of outlying observations. Our proposal is based on the idea of modelling the process as a scale mixture between a Gaussian and log-Gaussian process. And the novelty is to allow the scale process to vary as a function of covariates. The resultant model has a nonstationary covariance structure in space. Moreover, the resultant kurtosis varies with location, allowing the time series at each location to have different distributions with different tail behaviour. Inference procedure is performed under the Bayesian framework. The analysis of an artificial dataset illustrates how this proposal is able to capture heterogeneity in space caused by dependence on some spatial covariate or by a transformation of the process of interest. Furthermore, an application to maximum temperature data observed in the Spanish Basque country illustrates the effects of altitude in the variability of the process and how our proposed model identifies this dependence through parameters which can be interpreted as regression coefficients in the variance model.