Joint Department of Statistics/MIDAS Seminar: David S. Matteson, Assistant Professor, Department of Statistical Science and Social Statistics, Cornell University

Ambulance demand estimation at fine time and location scales is critical for fleet management and dynamic deployment. We are first 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.

For huge datasets, such as Melbourne, Australia, we propose an alternative predictive spatio-temporal kernel warping method. To predict hourly demand, we build a kernel density estimator using a sparse set of the most similar data from relevant past time periods (labeled data), but warp these kernels to a larger set of historical data regardless of time periods (point cloud). The point cloud represents the spatial structure and geographical characteristics of Melbourne, including complex boundaries, road networks, and neighborhoods. Borrowing from manifold learning, kernel warping is performed through a graph Laplacian of the point cloud and can be interpreted as a regularization towards, and a prior imposed, for spatial features. Kernel bandwidth and degree of warping are efficiently estimated via cross-validation, and can be made time- and/or location-specific.

The proposed models are 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. Our manuscripts are available online ( http://dx.doi.org/10.1080/01621459.2014.941466 and http://arxiv.org/abs/1507.00363).