Center for Statistical Sciences Seminar
Gene-environment interaction is of great scientific interest, but it is hard to assess especially for rare diseases. Strong modeling assumptions thus become inevitable for reasonable statistical efficiency, making the issue of bias-variance trade-off particularly pronounced and critical. In an attempt to achieve automated bias-variance trade-off, Mukherjee and Chatterjee (2008, Biometrics, Vol. 64, 685-694) proposed an exceedingly appealing estimator, derived from a heuristic empirical partially Bayes argument. The estimator, if it could achieve what it is designed for, would amount to another ``Stein's Paradox,'' providing practitioners with a powerful tool to combat the common and frustrating issue of bias-variance trade-off. But does this estimator deliver in general what was hoped for? This talk presents an investigation of this question, from both research and pedagogical perspectives. The research part is taken from Meng (2009) ``Automated Bias-variance Trade-off: Intuitive Inadmissibility or Inadmissible Intuition?'' (Frontiers of Statistical Decision Making and Bayesian Analysis, Eds: Chen et. al.; Springer; 95-112), and the pedagogical part is from Blitzstein and Meng (2010) ``Nano-Project Qualifying Exam Process: An Intensified Dialogue Between Students and Faculty'' (American Statistician, Vol. 64, 282-290).
[The two articles are available as Publications II. 13 and 0.11 respectively at http://www.stat.harvard.edu/Faculty_Content/Meng-cv.pdf or by emailing firstname.lastname@example.org]
Lefschetz Center for Dynamical Systems Seminar
Abstract: A recent ``Lax-Mizohata'' theorem of Guy Metivier states that for quasi-linear first-order systems, the Cauchy problem is well-posed only if the principal symbol is hyperbolic. I will discuss joint results with Nicolas Lerner, Toan Nguyen, Lu Yong and Marta Strani, that extend Metivier's theorem in various directions. Our approach consists in detecting instabilities from growth properties of the micro-local linear flow. Examples based on the Burgers, Van der Waals, Klein-Gordon-Zakharov, and Euler-Maxwell equations illustrate the results.
BU/Brown PDE Seminar
In this talk I will briefly describe the Smoluchowski and Doi Models describing a particle which will model some protein diffusing in a bounded domain (the cell) which reacts by binding with some subdomain, or more specifically, its boundary. The Doi model has a large parameter in it and we show that as the parameter tends to infinity, the solution to this model converges at some rate depending on the smoothness of the initial data.
Laura Silvinski (Brown): Lagrangian data assimilation and its application to geophysical fluid flows
Although Lagrangian trajectories of fluid parcels in the ocean can be modeled with systems of partial differential equations, the exact initial conditions of the relevant variables are unknown. Data assimilation uses knowledge of the locations of physical drifters to predict and update the probability distribution of initial conditions. In this talk I will present an overview of data assimilation, focusing on the Ensemble Kalman Filter in particular. In addition, I will discuss how knowledge of the underlying flow might be used to improve the accuracy of data assimilation schemes by giving insight into the optimal locations of drifter deployment. Finally, I will present some numerical results of the Ensemble Kalman Filter applied to the 2D Shallow Water Equations.
Anna Barry (BU): Vortex crystals in an inviscid fluid
Vortex Crystals are vortex configurations which evolve without changing shape or size. The main focus of this talk will be on the point vortex approximation for a two-dimensional inviscid fluid, and more specifically, vortex crystals occurring in the (1 + N )-vortex problem. Several applications of the theory will be explored.
Kelly McQuighan (Brown): Oscillons near a Forced Hopf Bifurcation
Oscillons are planar, spatially localized, temporally oscillating, radially symmetric struc- tures. We present a proof of the existence of oscillons in the forced planar complex Ginzburg- Landau equation through a geometric blow-up analysis. Our analysis is complemented by a numerical continuation study of oscillons in the forced Ginzburg-Landau equation using Matlab and AUTO.
Time: 3:30 - 5:30 pm
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