UIUC Dept. of Mathematics Seminar Calendar

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Thursday, January 12, 2012

Mathematics Colloquium - Special Lecture 2011-12
2:00 pm in 345 Altgeld Hall, Thursday, January 12, 2012

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Robert Erhardt (University of North Carolina, Chapel Hill)
Approximate Bayesian Computing for Spatial Extremes
Abstract: Statistical analysis of max-stable processes used to model spatial extremes has been limited by the difficulty in calculating the joint likelihood function. This precludes all standard likelihood-based approaches, including Bayesian approaches. In this paper we present a Bayesian approach through the use of approximate Bayesian computing. This circumvents the need for a joint likelihood function by instead relying on simulations from the (unavailable) likelihood. This method is compared with an alternative approach based on the composite likelihood. When estimating the spatial dependence of extremes, we demonstrate that approximate Bayesian computing can provide estimates with a lower mean square error than the composite likelihood approach, though at an appreciably higher computational cost. We also illustrate the performance of the method with an application to US temperature data to estimate the risk of crop loss due to an unlikely freeze event.

Mathematics Colloquium - Special Lecture 2011-12
4:00 pm in 245 Altgeld Hall, Thursday, January 12, 2012

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Jianfeng Lu (Courant Institute of Mathematical Sciences, New York University)
Efficient algorithm for electronic structure calculations
Abstract: Electronic structure theories, in particular Kohn-Sham density functional theory, are widely used in computational chemistry and material sciences nowadays. The computational cost using conventional algorithms is however expensive which limits the application to relative small systems. This calls for development of efficient algorithms to extend the first principle calculations to larger system. In this talk, we will discuss some recent progress in efficient algorithms for Kohn-Sham density functional theory. We will focus on the choice of accurate and efficient discretization for Kohn-Sham density functional theory.