Events

Min Yang, Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, will give a colloquium titled, "On Data Reduction of Big Data" at 4:15 PM in 127 Hayes-Healy Center.

Abstract…

Tingting Tang
University of Notre Dame
 

3:30 PM
154 Hurley Hall

"A Numerical Methods For Solving Elliptic Equations On Real Closed Algebraic Curves and Surfaces"

We develop a novel approach which combines numerical algebraic geometry and finite difference scheme to solve elliptic partial differential equations defined on real closed algebraic curves and surfaces. In particular, we use the numerical algebraic methods to discretize the domain then utilize local parameterization to design a special metric tensor which greatly simplifies the Laplacian-Beltrani operator on the local manifold at every mesh point. Finally, we apply standard finite difference scheme to the simplified differential equation system. The performance of this method is demonstrated through elliptic PDEs defined on smooth or singular closed algebraic sets.…

Alex Gorodetsky
University of Michigan
 

3:15 PM
154 Hurley Hall

"Mulitfidelity Uncertainty Quantification Through Approximate Control Variates and Bayesian Networks"

We consider algorithms for propagating uncertainty through computational simulation models of varying fidelities. Our goal is to estimate, or predict, quantities of interest from a specified high-fidelity model when only a limited number of these simulations is available. To aid in this task, lower fidelity models can be used to reduce the uncertainty of the high-fidelity predictions. We discuss several new developments we have made in these areas that include a new generalized approximate control variate sampling approach and a Bayesian network-based higher-order approach. The approximate control variate approach develops a framework for obtaining statistical estimators that have reduced variance with respect to Monte Carlo in cases where the control variates have unknown means. Our approach is motivated by certain sub-optimality properties of common multifidelity sampling techniques that include multilevel, multi-index, and multifidelity Monte Carlo; we show that each of these existing techniques cannot reach the variance reduction performance that would be achieved by an optimal linear control variate scheme. We then describe a new framework for computing approximate control variate estimators that does converge to the optimal linear control variate and that can also achieve orders of magnitude reduction in estimator variance relative to existing approaches.…

Yuehua Cui, Department of Statistics and Probability, Michigan State University, will give a colloquium titled, "Kernel based methods for genomic data analysis" at 4:15 PM in 127 Hayes-Healy Center.

Abstract

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Peter McCullagh
University of Chicago

3:30 PM
154 Hurley Hall

Statistical Sparsity

The first goal of this work is to offer a definition of sparsity that is faithful to current usage in the statistical literature. The second goal is to develop an asymptotic approximation for the conditional distribution of the signal $X$ given the observation $Y=X+\varepsilon$ for a sample of size one in an additive Gaussian model with known variance. Sparseness of the signal distribution is defined by the limiting exceedance rate for fixed thresholds, and distributional approximations are asymptotic in the sparsity rate $\rho \to 0$. The exceedance measure and its zeta transformation play a crucial inferential role: asymptotically, every posterior integral within a certain class depends only on the zeta function.…

Catalin Trenchea, Department of Mathematics, University of Pittsburgh, will give a colloquium titled, "TBD" at 4:15 PM in 127 Hayes-Healy Center.

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Alireza Doostan, Center for Aerospace Structures, University of Colorado, Boulder, will give a colloquium titled, "TBD" at 4:15 PM in 127 Hayes-Healy Center.

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Paul Bressloff, Department of Mathematics, University of Utah, will give a John A. Lynch Lecture titled, "TBD" at 4:00 PM in 105 Jordan Hall of Science.

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Guantao Chen, Dept. of Mathematics & Statistics, Georgia State University, will give a colloquium titled, "TBD" at 4:15 PM in 127 Hayes-Healy Center.

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Christopher Wikle, Dept. of Statistics, University of Missouri, will give a colloquium titled, "TBD" at 4:15 PM in 127 Hayes-Healy Center.

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