Keynote address

Recent Developments in Nonparametric Hierarchical Bayesian Modeling Michael I. Jordan Departments of EECS and Statistics, University of California, Berkeley Much statistical research is concerned with controlling some form of tradeoff between flexibility and variability. In Bayesian statistics, such control is often exerted via hierarchies---stochastic relationships among prior distributions. Nonparametric Bayesian statisticians work with priors that are general stochastic processes (e.g., distributions on spaces of continuous functions, spaces of monotone functions, or general measure spaces). Thus flexibility is emphasized and it is of particular importance to exert hierarchical control. In this talk I discuss Bayesian hierarchical modeling in the setting of two particularly interesting stochastic processes: the Dirichlet process and the Beta process. These processes are discrete with probability one, and have interesting relationships to various random combinatorial objects. They yield models with open-ended numbers of "clusters" and models with open-ended numbers of "features," respectively. I discuss Bayesian modeling based on hierarchical Dirichlet process priors and hierarchical Beta process priors, and present applications of these models to problems in bioinformatics, information retrieval and computational vision. [Joint work with Yee Whye Teh and Romain Thibaux.] ------- Michael Jordan is Professor in the Department of Electrical Engineering and Computer Science and the Department of Statistics at the University of California, Berkeley. He received his Masters from Arizona State University, and earned his PhD from the University of California, San Diego. He was a professor at the Massachusetts Institute of Technology for eleven years. Prof. Jordan's research has spanned the fields of statistics, computer science, electrical engineering, cognitive science and computational biology. He is the author of more than 250 publications in these fields. He has made contributions to the topics of graphical models, variational inference, nonparametric Bayesian modeling and kernel-based pattern recognition. He has also run an experimental laboratory in human motor learning. His work on graphical models has had significant impact on several applied research communities, finding applications to problems in information retrieval, image processing, network analysis and medical diagnosis. Prof. Jordan is a Fellow of the IMS, a Fellow of the IEEE and a Fellow of the AAAI. He was named an Institute Medallion Lecturer by the IMS in 2004.