Brown University Center for Statistical Sciences Seminar
- Reception following seminar at 167 Angell Street, 2nd floor conference |
Abstract: Case-control studies often rely on subjects to report their own exposure or treatment information: this information is often obtained from cases after the event of interest has occurred. This is problematic for mortality outcomes, because dead subjects cannot report the desired information. To avoid this problem, Weiss and Lazovich (1996, American Journal of Epidemiology 143, 319-322) proposed obtaining exposure information from potential cases, i.e., subjects diagnosed with disease, at the time of disease diagnosis, and also from a referent series. The design is best viewed as a new scheme for sampling from a cohort. We set forth assumptions that allow valid estimation of the effect of a time-varying exposure on mortality from these designs, and we show how to estimate those effects. Even when the sampling fraction of non-diseased subjects is unknown, causal risk ratios are estimable if diagnosis is rare in the cohort. We illustrate and compare conventional and new methods with data from a hypothetical study of breast cancer mortality and show how the new conceptualization can guide the design of these studies.
Stochastic Systems Seminar
Brown Applied Mathematics Pattern Theory and Vision Seminar
Abstract: A probabilistic method for tracking 3D articulated human figures in monocular image sequences is presented. Within a Bayesian framework, we define a generative model of image appearance, a robust likelihood function based on image graylevel differences, and a prior probability distribution over pose and joint angles that models how humans move. The posterior probability distribution over model parameters is represented using a discrete set of samples and is popagated over time using particle filtering. The approach extends previous work on parameterized optical flow estimation to exploit a complex 3D articulated motion model. It also extends previous work on human motion tracking by including a perspective camera model, by modeling limb self occlusion, and by recovering 3D motion from a monocular sequence. The explicit posterior probability distribution represents ambiguities due to image matching, model singularities, and perspective projection. The method relies only on a frame-to-frame assumption of brightness constancy and hence is able to track people under changing viewpoints, in grayscale image sequences, and with complex unknown backgrounds.
Joint work with: Hedvig Sidenbladh (Royal Institute of Technology, Sweden) David Fleet (Xerox PARC), Dirk Ormoneit (Stanford, Department of Statistics)
PDE Seminar
Abstract: Since Onsager's paper of 1949, several equilibrium statistical models have been proposed to explain the formation of large-scale, long-lived flow structures in two-dimensional turbulence. These include the Joyce-Montgomery point vortex model, the Kraichnan energy-enstrophy model, and the Miller-Robert continuum model. In this context I will formulate a model that retains the simplicity of ideal dynamics and equilibrium theory, while it discards any extraneous assumptions about the small-scale statistics.
Surprisingly, the canonical and microcanonical ensembles with respect to the global invariants (energy and circulation) are not always equivalent in a continuum model of this kind. In fact, there are regimes of real physical interest for which the microcanonical equilibrium states are richer than the canonical ones. This fact is closely related to classical hydrodynamical stability theory, which breaks down precisely in the nonequivalent regime. Motivated by the statistical approach I will show how to construct Lyapunov functionals in cases where the usual construction of Arnold does not apply. As an illustration of this phenomenon, I will present computations of quasi-geostrophic flows that represent the zonal jets and embedded spots in a Jovian atmosphere. These nonlinearly stable flows are the most probable states in the microcanonical model, even though they are omitted by the canonical model and lie beyond the classical sufficent conditions for stability.
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