  Predicting ambulance demand accurately at a fine resolution in time and space
(e.g., every hour and 1 km$^2$) is critical for staff / fleet management and
dynamic deployment. There are several challenges: though the dataset is
typically large-scale, demand per time period and locality is almost always
zero. The demand arises from complex urban geography and exhibits complex
spatio-temporal patterns, both of which need to captured and exploited. To
address these challenges, we propose three methods based on Gaussian mixture
models, kernel density estimation, and kernel warping. These methods provide
spatio-temporal predictions for Toronto and Melbourne that are significantly
more accurate than the current industry practice.
