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

TL;DR

This paper develops a non-separable spatio-temporal intensity model for ambulance interventions on linear networks, specifically applied to Milan, improving accuracy over traditional planar models.

Contribution

It introduces a novel non-separable first-order intensity function for events on linear networks, combining semi-parametric temporal estimation with non-parametric spatial modeling.

Findings

Model captures space-time interaction effectively.

Outperforms planar and separable models in fit accuracy.

Provides insights into ambulance intervention patterns.

Abstract

The algorithms used for the optimal management of an ambulance fleet require an accurate description of the spatio-temporal evolution of the emergency events. In the last years, several authors have proposed sophisticated statistical approaches to forecast ambulance dispatches, typically modelling the data 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 on a linear network. The constrained spatial domain raises specific challenges and unique methodological problems that cannot be ignored when developing a proper statistical approach. Hence, this paper proposes a spatio-temporal model to analyse ambulance dispatches focusing on the 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 dimension is estimated semi-parametrically using a Poisson regression model, while the spatial dimension is estimated non-parametrically 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 tests show that our approach successfully models the ambulance interventions and captures the space-time patterns more accurately than planar or separable point process models.