A Spatio-Temporal Point Process Model for Ambulance Demand

TL;DR

This paper introduces a novel spatio-temporal Gaussian mixture model for estimating ambulance demand in Toronto, capturing complex dynamics and seasonality, leading to significantly improved predictive accuracy over industry standards.

Contribution

The paper proposes a fixed-component Gaussian mixture model with time-varying weights and a birth-death MCMC extension for estimating demand, addressing data sparsity and seasonality.

Findings

Higher predictive accuracy than industry practice

Reduces EMS operational prediction error by up to two-thirds

Effectively models weekly and daily seasonality and short-term dependence

Abstract

Ambulance demand estimation at fine time and location scales is critical for fleet management and dynamic deployment. We are motivated by the problem of estimating the spatial distribution of ambulance demand in Toronto, Canada, as it changes over discrete 2-hour intervals. This large-scale dataset is sparse at the desired temporal resolutions and exhibits location-specific serial dependence, daily and weekly seasonality. We address these challenges by introducing a novel characterization of time-varying Gaussian mixture models. We fix the mixture component distributions across all time periods to overcome data sparsity and accurately describe Toronto's spatial structure, while representing the complex spatio-temporal dynamics through time-varying mixture weights. We constrain the mixture weights to capture weekly seasonality, and apply a conditionally autoregressive prior on the mixture weights of each component to represent location-specific short-term serial dependence and daily seasonality. While estimation may be performed using a fixed number of mixture components, we also extend to estimate the number of components using birth-and-death Markov chain Monte Carlo. The proposed model is shown to give higher statistical predictive accuracy and to reduce the error in predicting EMS operational performance by as much as two-thirds compared to a typical industry practice.