Colloquium/Seminar
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Event(s) on January 2008
- Thursday, 3rd January, 2008
Title: Asymptotic Normality of Multivariate Plug-in Level Set Estimates Speaker: Prof. Wolfgang Polonik, Department of Statistics, University of California, Davis, USA Time/Place: 14:30 - 15:30
FSC 1217Abstract: Level sets are regions where a multivariate target function f exceeds a given threshold value c. Such sets play a vital role in various fields of applications, such as anomaly detection, astronomical sky surveys, flow cytometry, and image segmentation. More statistical applications include classification and visualization of multivariate densities. Different types of level set estimates have been considered in the literature recently. Ingenious algorithms have been devised for fast computation, and consistency and (optimal and ‘fast’) rates of convergence have been derived for such level set estimates. While these results are interesting from a theoretical and computational point of view, they are not too helpful for statistical inference. In this talk we will address this problem of inference for level sets by focusing on a plug-in estimator C_n(c) = {x : f_n(x) ≥ c} of a density level set C(c) = {x : f(x) ≥ c}, where fn denotes a kernel density estimator of f. As a distance measure we consider the set-theoretic difference between C_n(c) and C(c), which is d_G(C_n(c),C(c)) = G(C_n(c) ∆ C(c)) = G(C_n(c) C(c)) + G(C(c) C_n(c)). We present and discuss conditions under which such plug-in estimates are asymptotically normal, in the sense that there exists a sequence of normalizing constants an and constants μ, σ^2 with σ^2 ≥ 0 such that an(d_G(C_n(c),C(c)) – μ) → dN(0, σ^2) as n → ∞. - Tuesday, 15th January, 2008
Title: Response-Adaptive Designs and Their Applications Speaker: Dr. Feifang Hu, Department of Statistics, University of Virginia, USA Time/Place: 11:30 - 12:30
FSC 1217Abstract: While clinical trials may provide information on new treatments that can impact countless lives in the future, the act of randomization means that volunteers in the clinical trial will receive the benefit of the new treatment only by chance. In most clinical trials, an attempt is made to balance the treatment assignments equally, thus the probability that a volunteer will receive the potentially better treatment is only 50%. Response-adaptive randomization (RAR) uses accruing data to skew the allocation probabilities to favor the treatment performing better thus far in the trial, thereby mitigating the problem to some degree. In this talk, I give a brief review of adaptive randomization. Then I propose some new response-adaptive randomization procedures that have some desirable properties. The resulting randomization procedures provide efficient methods to determine whether a new treatment is effective in a clinical trial, while simultaneously minimizing a clinical trial volunteer's chance of being assigned to the inferior treatment. We then discuss some important applications, some recent developments and further research topics. - Wednesday, 23rd January, 2008
Title: A Robust High Resolution Solver for Steady Euler Equations on Unstructured Grids Speaker: Mr. Guanghui Hu, Department of Mathematics, Hong Kong Baptist University, Hong Kong Time/Place: 10:30 - 11:30
FSC 1217Abstract: A high-order and robust algorithm is proposed to solve steady Euler equations on unstructured grids. The main ingredients of the algorithm include a standard Newton method as the outer iterative scheme and a linear multigrid method as the inner iterative scheme with the block lower-upper symmetric Gauss-Seidel (LU-SGS) iteration as its smoother. The Jacobian matrix of Newton-iteration is regularized by the local residual, instead of using the commonly adopted time-stepping relaxation technique based on the local CFL number. The local Jacobian matrix of the numerical fluxes are computed using the numerical differentiation, which can simplify the implementations significantly by comparing with the manually derived approximate derivatives. The polynomials on each cell are reconstructed by using the mean values of the numerical solutions; and higher-order reconstruction is realized by recursively applying the linear reconstruction method. It is found that the proposed algorithm is insensitive to the parameters used: In our computations, only one set of the three parameters is employed for various geometrical configurations and Mach numbers. The high-resolution and robustness of our algorithm are illustrated by considering two-dimensional airfoil problems with different geometrical configurations and Mach numbers. - Wednesday, 23rd January, 2008
Title: Testing for Smoothing Spline Models: An Variance Component Testing Approach Speaker: Mr. Ziqing Chang, Department of Mathematics, Hong Kong Baptist University, Hong Kong Time/Place: 14:30 - 15:30
FSC 1217Abstract: In this paper, we investigate model checking for smoothing spline models. In terms of transferring the hypothesis to an equivalent hypothesis that the variance of difference between the hypothetical and alternative models is equal to zero, a U-type test is defined and asymptotic behavior is investigated. The limiting null distribution is tractable and the test can detect alternatives converging to the null at parametric rate. A simulation study is performed for a comparison with existing tests. - Wednesday, 23rd January, 2008
Title: Statistical Inference for the Correlated Data from Paired Organs Speaker: Ms. Yanbo Pei, Department of Mathematics, Hong Kong Baptist University, Hong Kong Time/Place: 15:30 - 16:30
FSC 1217Abstract: In many medical comparative studies (e.g., comparison of two treatments in an otolaryngological study), subjects may produce either bilateral (e.g., responses from a pair of ears) or unilateral (response from only one ear) data. For bilateral cases, it is meaningful to assume that the information between the two ears from the same subject are generally highly correlated. In our article, we develop and evaluate different confidence interval estimators for the difference of two proportions to the bilateral data and different testing procedures for the difference of two proportions to the combined unilateral and bilateral data basing on different model assumption. - Monday, 28th January, 2008
Title: Artificial Boundary Method for Two-Dimensional Burgers Equation Speaker: Mr. Jiwei Zhang, Department of Mathematics, Hong Kong Baptist University, Hong Kong Time/Place: 15:30 - 16:30
FSC 1217Abstract: The numerical solution of the two-dimensional Burgers equation in unbounded domains is considered. By introducing a circular artificial boundary, we consider the initial-boundary problem on the disc enclosed by the artificial boundary. Based on the Cole-Hopf transformation and Fourier series expansion, we obtain the exact boundary condition and a series of approximating boundary conditions on the artificial boundary. Then the original problem is reduced to an equivalent problem on the bounded domain. Furthermore, the stability of the reduced problem is obtained. Finally, the finite difference method is applied to the reduced problem, and some numerical examples are given to demonstrate the feasibility and effectiveness of the approach.