A probabilistic spatio-temporal neural network to forecast COVID-19 counts

Geo-referenced and temporal data are becoming more and more ubiquitous in a wide range of fields such as medicine and economics. Particularly in the realm of medical research, spatio-temporal data play a pivotal role in tracking and understanding the spread and dynamics of diseases, enabling researchers to predict outbreaks, identify hot spots, and formulate effective intervention strategies. To forecast these types of data we propose a Probabilistic Spatio-Temporal Neural Network that (1) estimates, with computational efficiency, models with spatial and temporal components; and (2) combines the flexibility of a Neural Network-which is free from distributional assumptions-with the uncertainty quantification of probabilistic models. Our architecture is compared with the established INLA method, as well as with other baseline models, on COVID-19 data from Italian regions. Our empirical analysis demonstrates the superior predictive effectiveness of our method across multiple temporal ranges and offers insights for shaping targeted health interventions and strategies.