A non-separable first-order spatio-temporal intensity for events on linear networks: an application to ambulance interventions

The algorithms used for optimal management of ambulances require accurate description and prediction of the spatio-temporal evolution of emergency interventions. In the last years, several authors have proposed sophisticated statistical approaches to forecast the ambulance dispatches, typically modelling the events as a point pattern occurring on a planar region. Nevertheless, ambulance interventions can be more appropriately modelled as a realisation of a point process occurring along a network of lines, such as a road network. The constrained spatial domain raises specific challenges and unique methodological problems that cannot be ignored when developing a proper statistical model. Hence, this paper proposes a spatiotemporal model to analyse the ambulance interventions that occurred in the road network of Milan (Italy) from 2015 to 2017. We adopt a non-separable first-order intensity function with spatial and temporal terms. The temporal component is estimated semi-parametrically using a Poisson regression model, while the spatial dimension is estimated nonparametrically using a network kernel function. A set of weights is included in the spatial term to capture space-time interactions, inducing non-separability in the intensity function. A series of maps and graphical tests show that our approach successfully models the ambulance interventions and captures the space-time patterns.