$McMaster University$

Graduate Program in Statistics

SPEAKER:: Michael Escobar; Department of Public Health Sciences; University of Toronto

ABSTRACT:: This talk will discuss methods of finding individuals with unusual distributions of values. For example, with modern diagnostic equipment, one can measure the individual cell sizes from a sample of ones blood. It is believed that different illness can be characterized by the shape of the distribution of sizes of the red blood cells. In this talk, a hierarchical model for the distribution of the blood cells is developed. This model is somewhat equivalent to put a distribution on the family of kernel density estimates. Escobar and West (1995) showed how the kernel density estimator approximates a Bayesian method of estimating densities based on a mixture of Dirichlet processes (MDP). However, since the MDP method is a proper bayesian model, one can use hierarchical priors and calculate posterior distributions of functionals of interest. Using these techniques, we develop a highly flexible hierarchical model in the space of distributions. This model allows us to model samples of densities and to find outliers in the space of distributions. This talk will discuss the methods used to compute these models and to assess outliers. These techniques will be used to identify diseased subjects based on the distribution of the size of the subject's red blood cells. This talk is joint work with George Tomlinson and Christine McLaren

About the Speaker: Mike Escobar holds a joint appointment as associate professor in the Departments of Public Health Sciences and Statistics at University of Toronto. One of his main areas of theoretical research is in nonparametric Bayesian methods where he has developed methods for computing Dirichelet process models. Another area is the development of mixture models which can be used to model population heterogeneity. As well as theoretical research Dr. Escobar does a lot of research into the application of statistical methods in psychiatric research, especially in the areas of schizophrenia, learning disabilities, and suicide.
Dr. Escobar received his undergraduate training in mathematics from Tufts University. He received his Ph.D. in Statistics from Yale University where he worked under the supervision of Professor John A. Hartigan. His doctoral thesis won the Leonard J. Savage Thesis Award in 1988. He was an assistant professor at Carnegie Mellon University from 1990 to 1994 when he moved to the University of Toronto where he has remained since then.

References

Some background information related to this talk can be found in

Escobar, M.D. and West, M., "Bayesian Density Estimation and Inference Using Mixtures", Journal of the American Statistical Association, 1995, 90, 577-588.