  Predicting ambulance demand accurately at fine time and location scales is
critical for ambulance fleet management and dynamic deployment. Large-scale
datasets in this setting typically exhibit complex spatio-temporal dynamics and
sparsity at high resolutions. We propose a predictive method using
spatio-temporal kernel density estimation (stKDE) to address these challenges,
and provide spatial density predictions for ambulance demand in Toronto, Canada
as it varies over hourly intervals. Specifically, we weight the spatial kernel
of each historical observation by its informativeness to the current predictive
task. We construct spatio-temporal weight functions to incorporate various
temporal and spatial patterns in ambulance demand, including location-specific
seasonalities and short-term serial dependence. This allows us to draw out the
most helpful historical data, and exploit spatio-temporal patterns in the data
for accurate and fast predictions. We further provide efficient estimation and
customizable prediction procedures. stKDE is easy to use and interpret by
non-specialized personnel from the emergency medical service industry. It also
has significantly higher statistical accuracy than the current industry
practice, with a comparable amount of computational expense.
