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Slideshow

Tags: Colloquium Series

The Statistics Department hosts weekly colloquia on a variety of statistcal subjects, bringing in speakers from around the world.

http://philippe.barbe.perso.math.cnrs.fr
We present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in the data--functional, time dependent, and multivariate components--we extend hierarchical dynamic linear models for multivariate time series to the functional data setting. We also develop Bayesian spline theory in a more general constrained optimization framework. The proposed methods identify a time-…
We propose a learning algorithm for a class of random field models of natural image patterns, where the energy functions of the random fields are in the form of linear combinations of rectified filter responses from subsets of wavelets selected from a given over-complete dictionary. The algorithm consists of the following two components. (1) We propose to induce the wavelets into the random field model by a generative version of the epsilon-…
Understanding the complex dynamics of Earth's climate system is a grand scientific challenge. Projecting climate for 50 or 100 years into the future is, however, complicated by the fact that the behavior of the Earth system over such time scales is not well characterized over the modern instrumental interval, which only stretches back about 100-150 years with global extent. Paleoclimate reconstructions using climate proxies such as tree rings,…
We propose a nonparametric estimator of the dynamics of monotonically increasing or decreasing trajectories defined on a finite time interval. Such trajectories can be described as solutions of autonomous ODEs. Under suitable regularity conditions, we derive the optimal rate of convergence for the proposed estimator and show that it is the same as that for estimating the derivative of a trajectory. We also show that commonly used two-stage…
We propose a general theory and the estimation procedures for nonlinear sufficient dimension reduction where the predictor or the response, or both, are random functions. The relation between the response and predictor can be arbitrary and the sets of observed time points can vary from subject to subject. The functional and nonlinear nature of the problem leads naturally to consideration of two levels of functional spaces: the first space…
Much of forensic laboratory work is based on comparison of evidence from a crime scene with analogous material associated with a suspect. DNA samples and fingerprints are well-known examples, but physical evidence also includes such items as tire and shoe prints, and bullet metal components.  There is current concern in the legal system about the degree of objectivity that can be claimed by current forensic comparison practices.  In…
Complex diseases such as cancer have often heterogeneous responses to treatment, and this has attracted much interest in developing individualized treatment rules to tailor therapies to an individual patient according to the patient-specific  characteristics. In this talk, we discuss how to use Bayesian neural networks to achieve this goal, including how to select disease related features. The theoretical properties of Bayesian neural…
First, I will review the lasso method and show an example of its utility in cancer diagnosis via mass spectometry. Then I will consider the testing the significance of the terms in a fitted regression, fit via the lasso or forward stepwise regression. I will present a novel statistical framework for this problem, one that provides p-values and confidence intervals that properly account for the inherent selection in the fitting procedure. I will…
Statistics has played a key role in the development and validation of forensic methods, as well as in the inferences (conclusions) obtained from forensic evidence.  Further, statisticians have been important contributors to many areas of science, such as chemistry (chemometrics), biology (genomics), medicine (clinical trials), and agriculture (crop yield), leading to valuable advances that extend to multiple fields (spectral analysis,…

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