Title: Statistical models for the analysis, prediction and monitoring of space-time data. Applications to infectious diseases and crime
Abstract: We present several statistical approaches to understand the underlying temporal and spatial dynamics of infectious diseases (with a focus on Covid-19 data) that can result in informed and timely public health policies. Most studies in the context of infectious diseases commonly report figures of the overall infection at a state- or county-level, reporting the aggregated number of cases in a particular region at one time. However, we focus on analysing high-resolution Covid-19 datasets in form of spatio-temporal point patterns, offering vital insights for the spatio-temporal interaction between individuals concerning the disease spread in a metropolis.
We develop a non-stationary spatio-temporal point process, assuming that previously infected cases trigger newly confirmed ones, and introduce a neural network-based kernel to capture the spatially varying triggering effect. The neural network-based kernel is carefully crafted to enhance expressiveness while maintaining results interpretability. We also incorporate some exogenous influences imposed by city landmarks. Additionally, we propose some mechanistic models giving particular data-driven forms to the spatio-temporal intensity function. Particular cluster spatio-temporal models to identify unknown parents are also depicted. For completeness, we present a method to evaluate the direction and velocities of the spread by considering the intensity comes from a growth differential equation.
Crime science deals with the analysis of crime data from many perspectives. This type of data brings up a large variety of problems linked with data science and big data analysis. In general grounds, crime data provides heterogeneous patterns in space and time, and we present methods able to handle this heterogeneity. In particular, we consider statistical models to detect generators of crime in cities together with potential focuses that attract or inhibit crimes in a spatio-temporal region. We also consider methods to reduce potential large dimensionality in the data, and some artificial intelligent methods to help handling large amounts of crime data. Two final crucial probabilistic models will be presented. One is modelling crime data using stochastic point pattern processes, such as log-Gaussian Cox processes, that will be used to forecast and predict risk of crimes in subregions of space and time of a city. This aspect will be complemented with another type of stochastic models with differential equations governing the spread of a type of crime.