Spatio-temporal mixture process estimation to detect dynamical changes in population

Population monitoring is a challenge in many areas such as public health and ecology. We propose a method to model and monitor population distributions over space and time, in order to build an alert system for spatio-temporal data changes. Assuming that mixture models can correctly model populations, we propose a new version of the Expectation-Maximization (EM) algorithm to better estimate the number of clusters and their parameters at the same time. This algorithm is compared to existing methods on several simulated datasets. We then combine the algorithm with a temporal statistical model, allowing for the detection of dynamical changes in population distributions, and call the result a spatio-temporal mixture process (STMP). We test STMPs on synthetic data, and consider several different behaviors of the distributions, to fit this process. Finally, we validate STMPs on a real data set of positive diagnosed patients to coronavirus disease 2019. We show that our pipeline correctly models evolving real data and detects epidemic changes.