Gaussian Processes for Spatiotemporal Modelling

A statistical framework for spatiotemporal modelling should ideally be able to assimilate different types of data from different of sources. Gaussian processes are commonly used tool for interpolating values across time and space domains. In this thesis we work on extending the Gaussian processes framework to deal with diverse noise model assumptions. We present a model based on a hybrid approach that combines some of the features of the discriminative and generative perspectives, allowing continuous dimensionality reduction of hybrid discrete-continuous data, discriminative classification with missing inputs and manifold learning informed by class labels. We present an application of malaria density modelling across Uganda using administrative records. This disease represents a threat for approximately 3.3 billion people around the globe. The analysis of malaria based on the records available faces two main complications: noise induced by a highly variable rate of reporting health facilities; and lack of comparability across time, due to changes in districts delimitation. We define a Gaussian process model able to assimilate this features in the data and provide an insight on the generating process behind the records. Finally, a method to monitor malaria case-counts is proposed. We use vector-valued covariance kernels to analyze the time series components individually. The short term variations of the infection are divided into four cyclical phases. The graphical tool provided can help quick response planning and resources allocation.