Research Description (Woodard)

Statistics:

Bayesian statistical methods and applications. Clustering methods, functional data analysis, time series models, and estimation on road networks. My primary application area is statistical estimation for operations and management problems. For instance, I work on forecasting demand for ambulance services, in space and time. Huge amounts of historical data are available, and fine-scale forecasts are required since ambulance demand varies dramatically in time and by locality. I also collaborate with researchers at Microsoft on statistical and data mining methods for managing datacenters. These centers are the backbone of much of modern computing infrastructure. They are too large and complex to be managed via manual monitoring and control, so the real-time analysis of data regarding system status and demand is critical.

Applied Probability & Algorithm Analysis:

I use probability tools to analyze the efficiency of computational methods that are used in Bayesian statistics. These primarily consist of Markov chain Monte Carlo and “adaptive Markov chain” methods. I analyze how the efficiency of these methods scales with the difficulty of the problem, such as the number of observations or the number of parameters in the statistical model. For instance, in the context of estimation in a genomics model, it is desirable to obtain accurate estimates in time linear in the length of the DNA sequence. In the context of estimating travel times on a road network, it is important that the time required for accurate estimation grows linearly, or at most polynomially, as a function of the number of road segments in the network.