The New England Journal of Statistics in Data Science

Graphical models have witnessed significant growth and usage in spatial data science for modeling data referenced over a massive number of spatial-temporal coordinates. Much of this literature has focused on a single or relatively few spatially dependent outcomes. Recent attention has focused upon addressing modeling and inference for substantially large number of outcomes. While spatial factor models and multivariate basis expansions occupy a prominent place in this domain, this article elucidates a recent approach, graphical Gaussian Processes, that exploits the notion of conditional independence among a very large number of spatial processes to build scalable graphical models for fully model-based Bayesian analysis of multivariate spatial data.

In this paper, we build a mechanistic system to understand the relation between a reduction in human mobility and Covid-19 spread dynamics within New York City. To this end, we propose a multivariate compartmental system that jointly models smartphone mobility data and case counts during the first 90 days of the epidemic. Parameter calibration is achieved through the formulation of a general statistical-mechanistic Bayesian hierarchical model. The open-source probabilistic programming language Stan is used for the requisite computation. Through sensitivity analysis and out-of-sample forecasting, we find our simple and interpretable model provides quantifiable evidence for how reductions in human mobility altered early case dynamics in New York City.