IMA Journal of Management Mathematics (2022) 33, 101–121 https://doi.org/10.1093/imaman/dpaa028 Advance Access publication on 13 January 2021 Bayesian spatio-temporal modelling and prediction of areal demands for ambulance services Vittorio Nicoletta † Department of Operations and Decision Systems, Université Laval, Québec G1V 0A6, Canada † Corresponding author. Email: vittorio.nicoletta.1@ulaval.ca Alessandra Guglielmi Dipartimento di Matematica, Politecnico di Milano, Milan 20133, Italy Angel Ruiz Department of Operations and Decision Systems, Université Laval, Québec G1V 0A6, Canada Valérie Bélanger Department of Logistics and Operations Management, HEC Montréal, Montréal H3T 2A7, Canada and Ettore Lanzarone Department of Management, Information and Production Engineering, University of Bergamo, Dalmine (BG) 24044, Italy [Received on 29 May 2019; accepted on 24 November 2020] Careful planning of an ambulance service is critical to reduce response times to emergency calls and make assistance more effective. However, the demand for emergency services is highly variable, and good prediction of the number of future emergency calls, and their spatial and temporal distribution, is challenging. In this work, we propose a Bayesian approach to predict the number of emergency calls in future time periods for each zone of the served territory. The number of calls is described by a generalized linear mixed effects model, and inference, in terms of posterior predictive distributions, is obtained through Markov chain Monte Carlo simulation. Our approach is applied in a large city in Canada. The paper demonstrates that using a model for areal data provides good results in terms of predictive accuracy and allows flexibility in accounting for the main features of the dataset. Moreover, it shows the computational efficiency of the approach despite the huge dataset. Keywords: emergency medical services; exchangeable prior; hierarchical models; Markov chain Monte Carlo; posterior predictive distribution. 1. Introduction Emergency medical services (EMSs) consist of pre-hospital medical care and ambulance transport to a medical facility (Ingolfsson, 2013). Almost all EMS requests arrive by phone, through calls to an emergency number. The urgency of each request is evaluated and the location of the call is obtained. If the request is worthy of an intervention, an ambulance is dispatched to the call site; then, if needed, the patient is transported to a medical facility. Demand for such services is constantly increasing throughout the world, according to population growth and ageing, while we observe a continuous pressure of © The Author(s) 2021. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. Downloaded from https://academic.oup.com/imaman/article/33/1/101/6093863 by guest on 08 January 2023