Abstract
Dirichlet processes and their extensions have reached a great popularity in Bayesian nonparametric statistics. They have also been introduced for spatial and spatio-temporal data, as a tool to analyze and predict surfaces. A popular approach to Dirichlet processes in a spatial setting relies on a stick-breaking representation of the process, where the dependence over space is described in the definition of the stick-breaking probabilities. Extensions to include temporal dependence are still limited, however it is important, in particular for those phenomena which may change rapidly over time and space, with many local changes. In this work, we propose a Dirichlet process where the stick-breaking probabilities are defined to incorporate both spatial and temporal dependence. We will show that this approach is not a simple extension of available methodologies and can outperform available approaches in terms of prediction accuracy. The approach results in a predictive model that does not rely on the assumptions of Gaussianity or the separability of time and space.
Acknowledgments
The author would like to thank two anonymous reviewers, one Associate Editor and the Editor-in-chief of Bayesian analysis for constructive feedback and valuable suggestions. In particular, a reviewer recommended and provide suggestions for the derivation of the first part of the proof in Appendix A (i.e. ).
Citation
Clara Grazian. "Spatio-Temporal Stick-Breaking Process." Bayesian Anal. Advance Publication 1 - 32, 2024. https://doi.org/10.1214/24-BA1419
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