Modelling Non-Gaussian Spatio-Temporal Processes

In the analysis of most spatiotemporal processes in environmental studies, observations present distributions that are not normal. Commonly, some transformation is applied to the data and inference is performed at the transformed scale. Commonly, the transformation will have an impact on the description of the uncertainty at future instants of time or unobserved locations of interest.
In this talk I will discuss some of the projects I have been involved with in the last five years that relax the assumption of normality of spatiotemporal processes after some suitable transformation of the data. In particular, I will focus on a recent proposal that models the variance law of multivariate dynamic linear models. The proposed approach adds flexibility to the usual Multivariate Dynamic Gaussian model by defining the process as a scale mixture between a Gaussian and log-Gaussian processes. The scale is represented by a process varying smoothly over space and time which is allowed to depend on covariates. Analysis of artificial datasets show that the parameters are identifiable and simpler models are well recovered by the general proposed model. The analyses of two important environmental processes, maximum temperature and maximum ozone, illustrate the effectiveness of our proposal in improving the uncertainty quantification in the prediction of spatio-temporal processes.

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About Alexandra Schmidt

Alexandra M. Schmidt is Professor and Program Director of Biostatistics at McGill University.  She is an elected Fellow of the American Statistical Association and an elected member of the International Statistical Institute and was the 2015 President of the International Society for Bayesian Analysis. In 2017 she was awarded the Distinguished Achievement Medal Distinguished Achievement Medal (2017) from the American Statistical Association’s Section on Statistics and the Environment and in 2008 the Abdel El-Sharrawi Young Investigator Award from The International Environmetrics Society.