An information-theoretic approach to study spatial dependencies in small datasets

From epidemiology to economics, there is a fundamental need of statistically principled approaches to unveil spatial patterns and identify their underpinning mechanisms. Grounded in network and information theory, we establish a non-parametric scheme to study spatial associations from limited measurements of a spatial process. Through the lens of network theory, we relate spatial patterning in the dataset to the topology of a network on which the process unfolds. From the available observations of the spatial process and a candidate network topology, we compute a mutual information statistic that measures the extent to which the measurement at a node is explained by observations at neighbouring nodes. For a class of networks and linear autoregressive processes, we establish closed-form expressions for the mutual information statistic in terms of network topological features. We demonstrate the feasibility of the approach on synthetic datasets comprising 25-100 measurements, generated by linear or nonlinear autoregressive processes. Upon validation on synthetic processes, we examine datasets of human migration under climate change in Bangladesh and motor vehicle deaths in the United States of America. For both these real datasets, our approach is successful in identifying meaningful spatial patterns, begetting statistically-principled insight into the mechanisms of important socioeconomic problems.