Statistical Models to Incorporate Heterogeneity in Spatio-temporal Prediction by Clara Grazian
Dirichlet processes and their extensions have reached great popularity in Bayesian nonparametric statistics. They have also been introduced for spatial and spatio-temporal data, as a tool to analyse and predict surfaces.
A popular approach to the Dirichlet process in a spatial setting relies on a stick-breaking representation, where the dependence over space is described in the definition of the stick-breaking probabilities. Extensions to include temporal dependence usually introduce a temporal dependence among the atoms of the Dirichlet process, however this approach does not let us properly test and incorporate a possible interaction between space and time.
In this talk, a Dirichlet process is proposed where the stick-breaking probabilities are defined to incorporate both spatial and temporal dependence. An advantage of the method is that it offers a natural way to test for separability of the two components. The performance of this approach will be tested on simulations and a real-data example from meteorology.
Dr Clara Grazian received a joint PhD in 2016 from the University Paris-Dauphine, France and the Sapienza University of Rome, Italy, working on Bayesian analysis for mixture models and copula models. She then joined the Nuffield Department of Medicine and the Big Data Institute of the University of Oxford to work on an international project trying to investigate mechanisms of drug resistance developed by tuberculosis. Before joining the School of Mathematics and Statistics at the University of Sydney, Clara was Senior Lecturer in Statistics at the University of New South Wales. Her interests include both theoretical and applied aspects of Bayesian statistics, with applications in microbiology and environmental sciences.