A Hierarchical Spatio-Temporal Statistical Model Motivated by Glaciology

In this paper, we extend and analyze a Bayesian hierarchical spatio-temporal model for physical systems. A novelty is to model the discrepancy between the output of a computer simulator for a physical process and the actual process values with a multivariate random walk. For computational efficiency, linear algebra for bandwidth limited matrices is utilized, and first-order emulator inference allows for the fast emulation of a numerical partial differential equation (PDE) solver. A test scenario from a physical system motivated by glaciology is used to examine the speed and accuracy of the computational methods used, in addition to the viability of modeling assumptions. We conclude by discussing how the model and associated methodology can be applied in other physical contexts besides glaciology.Comment: Revision accepted for publication by the Journal of Agricultural, Biological, and Environmental Statistic

Biologically Inspired Dynamic Textures for Probing Motion Perception

Perception is often described as a predictive process based on an optimal inference with respect to a generative model. We study here the principled construction of a generative model specifically crafted to probe motion perception. In that context, we first provide an axiomatic, biologically-driven derivation of the model. This model synthesizes random dynamic textures which are defined by stationary Gaussian distributions obtained by the random aggregation of warped patterns. Importantly, we show that this model can equivalently be described as a stochastic partial differential equation. Using this characterization of motion in images, it allows us to recast motion-energy models into a principled Bayesian inference framework. Finally, we apply these textures in order to psychophysically probe speed perception in humans. In this framework, while the likelihood is derived from the generative model, the prior is estimated from the observed results and accounts for the perceptual bias in a principled fashion.Comment: Twenty-ninth Annual Conference on Neural Information Processing Systems (NIPS), Dec 2015, Montreal, Canad

Ambulance Emergency Response Optimization in Developing Countries

The lack of emergency medical transportation is viewed as the main barrier to the access of emergency medical care in low and middle-income countries (LMICs). In this paper, we present a robust optimization approach to optimize both the location and routing of emergency response vehicles, accounting for uncertainty in travel times and spatial demand characteristic of LMICs. We traveled to Dhaka, Bangladesh, the sixth largest and third most densely populated city in the world, to conduct field research resulting in the collection of two unique datasets that inform our approach. This data is leveraged to develop machine learning methodologies to estimate demand for emergency medical services in a LMIC setting and to predict the travel time between any two locations in the road network for different times of day and days of the week. We combine our robust optimization and machine learning frameworks with real data to provide an in-depth investigation into three policy-related questions. First, we demonstrate that outpost locations optimized for weekday rush hour lead to good performance for all times of day and days of the week. Second, we find that significant improvements in emergency response times can be achieved by re-locating a small number of outposts and that the performance of the current system could be replicated using only 30% of the resources. Lastly, we show that a fleet of small motorcycle-based ambulances has the potential to significantly outperform traditional ambulance vans. In particular, they are able to capture three times more demand while reducing the median response time by 42% due to increased routing flexibility offered by nimble vehicles on a larger road network. Our results provide practical insights for emergency response optimization that can be leveraged by hospital-based and private ambulance providers in Dhaka and other urban centers in LMICs