A Bayesian aoristic logistic regression to model spatio-temporal crime risk under the presence of interval-censored event times

From a statistical point of view, crime data present certain peculiarities that have led to a growing interest in their analysis. In particular, a characteristic that some property crimes frequently present is the existence of uncertainty about their exact location in time, being usual to only have a time window that delimits the occurrence of the event. There are different methods to deal with this type of interval-censored observation, most of them based on event time imputation. Another alternative is to carry out an aoristic analysis, which is based on assigning the same weight to each time unit included in the interval that limits the uncertainty about the event. However, this method has its limitations. In this paper, we present a spatio-temporal model based on the logistic regression that allows the analysis of crime data with temporal uncertainty, following the spirit of the aoristic method. The model is developed from a Bayesian perspective, which allows accommodating the temporal uncertainty of the observations. The model is applied to a dataset of residential burglaries recorded in Valencia, Spain. The results provided by this model are compared with those corresponding to the complete cases model, which discards temporally-uncertain events.