A Spatio-Temporal Point Process Model for Ambulance Demand

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

Measuring stochastic dependence using [phi]-divergence

The problem of bivariate (multivariate) dependence has enjoyed the attention of researchers for over a century, since independence in the data is often a desired property. There exists a vast literature on measures of dependence, based mostly on the distance of the joint distribution of the data and the product of the marginal distributions, where the latter distribution assumes the property of independence. In this article, we explore measures of multivariate dependence based on the [phi]-divergence of the joint distribution of a random vector and the distribution that corresponds to independence of the components of the vector, the product of the marginals. Properties of these measures are also investigated and we employ and extend the axiomatic framework of Renyi [On measures of dependence, Acta Math. Acad. Sci. Hungar. 10 (1959) 441-451], in order to assert the importance of [phi]-divergence measures of dependence for a general convex function [phi] as well as special cases of [phi]. Moreover, we obtain point estimates as well as interval estimators when an elliptical distribution is used to model the data, based on [phi]-divergence via Monte Carlo methods.Elliptical family of distributions Monte Carlo methods Multivariate dependence Renyi's axioms [phi]-divergence measures of dependence

Modeling shape distributions and inferences for assessing differences in shapes

The general class of complex elliptical shape distributions on a complex sphere provides a natural framework for modeling shapes in two dimensions. Such class includes many distributions, e.g., complex Normal, Watson, Bingham, angular central Gaussian and several others. We employ this class of distributions to develop methods for asserting differences in populations of shapes in two dimensions. Maximum likelihood and Bayesian methods for estimation of modal difference are developed along with hypothesis testing and credible regions for average shape difference. The methodology is applied in an example from biometry, where we are interested in detecting shape differences between male and female gorilla skulls.Complex elliptical family of distributions Complex Watson distribution HPD credible set Markov chain Monte Carlo Modal shape Shape distributions Average shape difference