Agenda

Alexandra Schmidt
McGill University

Abstract

Gaussian processes (GPs) are routinely used in the modelling of spatial and spatio-temporal processes. This is because they are fully specified by their mean and covariance functions, and prediction to unobserved locations easily follows from the properties of the partition of multivariate normal distributions. However, observations associated with environmental processes rarely follow a normal distribution. Although data are commonly transformed to attain normality, transformation can affect the quantification of uncertainty of predictions. I will discuss some spatial and spatiotemporal models for processes on their original scale. In particular, I will propose an extension of the popular multivariate dynamic linear model to accommodate heavy tails both for univariate and multivariate spatio-temporal processes. GPs require the evaluation of the determinant and inverse of covariance matrices, which becomes expensive as the number of observed sites grows large. As the proposed class of models involve more than one GP, inference can become computationally challenging when using Markov chain Monte Carlo methods to obtain samples from the resultant posterior distribution. To address this challenge, I will discuss how to approximate the proposed models when the number of observations across space is large. Examples using the proposed extensions include the analysis of temperature measurements across the Basque country, and the joint modelling of PM10 and ozone across the UK.

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This lecture is included in the programme of the 2024 ISBA World Meeting

For further information please contact isba2024@unive.it