A Sensitive Approach to Spatiotemporal Patterning in Urban Violent Crime by Tarun Yadav ’21, Mathematics Senior Thesis Defense, Tuesday, May 18, 1 – 1:45 pm, live talk can be accessed at https://williams.zoom.us/j/97617951870.
Abstract: Urban crime, as understood in modern criminology is a sociological, and further a sociogenic, phenomenon governed by complex, dynamic processes. Characteristics of the civic, social, and urban environment influence where and when crime events occur; however, past studies often analyse cross-sectional data for one spatial scale and do not account for the processes and place-based policies that influence crime across multiple scales. In this talk, we will discuss my thesis which, (i) builds a dataset for studying crime incidents in context over the last 10 years in the metropolitan area of Chicago, (ii) applies a Bayesian cross-classified multilevel modelling approach to examine the spatiotemporal patterning of violent crime in Chicago; and (iii) motivates directions, at the intersection of Bayesian computation and data assimilation, for supplementing theoretical work in mathematical criminology. Specifically, we will discuss a stochastic partial differential equations (SPDE) approach to the modelling of violent crime incidents as Gaussian spatial processes and the computational infrastructure that enables sparse approximations to solution Gaussian fields of the said SPDE such that Bayesian inference is computationally feasible.