Brown University Center for Statistical Sciences Seminar
Associate Professor, The George Washington University | |
(Refreshments beginning at 3:15 p.m.) |
Abstract: A popular summary measure of the discriminatory ability of a single continuous diagnostic marker for binary disease outcomes is the receiver-operator characteristics curve (ROC). For most diseases however, single biomarkers do not have adequate sensitivity or specificity for practical purposes. We present an approach to combine several markers into a composite diagnostic test without assuming a model for the distribution of the predictors. Using sufficient dimension reduction techniques, we replace the predictor vector with a lower-dimensional version, obtained through linear transformations of biomarkers, without loss of information. We show how to combine the linear transformations into a scalar diagnostic score whose performance can be assessed by the ROC curve. The asymptotic distribution of the left singular vectors of a consistent estimate of an asymptotically normally distributed random matrix is derived. It is used to construct an asymptotic chi-squared test to assess individual biomarker contribution to the diagnostic score. This talk will also include a brief overview of the sufficient dimension reduction (SDR) methodology.
Stochastic Systems Seminar
e-mail: eric.gautier@yale.edu | |
Abstract: Nonlinar schroinger (NLS) equations are generic models from physics describing the propagation of monochromatic wave packets in weakly nonlinear dispersive media (eg. nonlinear optical fibers, superfluid helium, anharmonic chains of atoms, crystals, Bose-Einstein condensates...). Stochastic NLS equations are often considered and noise account for thermal effects or amplification devices. We will first present the main results as well as large deviations for the small noise asymptotics. We will then present applications to blow-up times, evaluation of the error in soliton transmission and exit from a domain of attraction for weakly damped equations.
Brown University Center for Statistical Sciences Seminar
Psychology and Psychiatry, University of Illinois at Urbana-Champaign | |
Spectral Models: Applications in Brain signal Analysis | |
Refreshments at 3:15 p.m. |
Abstract: Part I. Observed fMRI data can be decomposed into the BOLD (blood oxygen level dependent) signal plus background noise. The BOLD signal is modeled as the convolution between the hemodynamic response function (HRF) and the stimulus (on-off) indicator. Since the effect of a stimulus may be as little as one percent of the BOLD signal, the statistical power of any activation detection methods relies on a properly specified HRF. The standard approach is to model the HRF parametrically as a difference between two gamma functions. This approach, however, assumes that the HRF is invariant across trials and across the entire brain volume. Empirical investigations in olfaction and visual studies suggest otherwise. Using functional mixed effects models, We present an alternative approach to estimating the ``global" HRF and variation across trials.
Part II. Brain signals are realizations of latent (unobserved) brain activity. A major goal of my research program is to develop models for the underlying or the driving spatio-temporal brain processes. We present an exploratory data analysis of optical images recorded in a switching task paradigm. We report preliminary results that suggest that the spectral distribution of the optical signals change smoothly across the brain. We will propose an integrated spatio-temporal-spectral model that also takes into account variation across subjects. The spatially-varying spectrum, which is the primary quantity of interest, can be estimated consistently by kernel smoothing.
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