Bayesian Nonparametric Methods for Complex Dynamical Phenomena – Emily Fox (University of Pennsylvania)
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Markov switching processes, such as hidden Markov models (HMMs) and switching linear dynamical systems (SLDSs), are often used to describe rich classes of dynamical phenomena. They describe complex temporal behavior via repeated returns to a set of simpler models: imagine, for example, a person alternating between walking, running and jumping behaviors, or a stock index switching between regimes of high and low volatility.Traditional modeling approaches for Markov switching processes typically assume a fixed, pre-specified number of dynamical models. Here, in contrast, I develop Bayesian nonparametric approaches that define priors on an unbounded number of potential Markov models. Using stochastic processes including the beta and Dirichlet process, I develop methods that allow the data to define the complexity of inferred classes of models, while permitting efficient computational algorithms for inference. The new methodology also has generalizations for modeling and discovery of dynamic structure shared by multiple related time series.Interleaved throughout the talk are results from studies of the NIST speaker diarization database, stochastic volatility of a stock index, the dances of honeybees, and human motion capture videos.
Emily B. Fox received the S.B. degree in 2004, M.Eng. degree in 2005, and E.E. degree in 2008 from the Department of Electrical Engineering and Computer Science at the Massachusetts Institute of Technology (MIT). She is currently an assistant professor in the Wharton Statistics Department at the University of Pennsylvania. Her Ph.D. was advised by Prof. Alan Willsky in the Stochastic Systems Group, and she recently completed a postdoc in the Department of Statistical Science at Duke University working with Profs. Mike West and David Dunson. Emily is a recipient of the National Defense Science and Engineering Graduate (NDSEG), National Science Foundation (NSF) Graduate Research fellowships, and NSF Mathematical Sciences Postdoctoral Research Fellowship. She has also been awarded the 2009 Leonard J. Savage Thesis Award in Applied Methodology, the 2009 MIT EECS Jin-Au Kong Outstanding Doctoral Thesis Prize, the 2005 Chorafas Award for superior contributions in research, and the 2005 MIT EECS David Adler Memorial 2nd Place Master’s Thesis Prize. Her research interests are in multivariate time series analysis and Bayesian nonparametric methods.