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Event(s) on January 2008
- 3/1/2008
| 題目: |
Asymptotic Normality of Multivariate Plug-in Level Set Estimates |
| 講員: |
Prof. Wolfgang Polonik, Department of Statistics, University of California, Davis, USA |
| 時間/地點: |
14:30 - 15:30
FSC 1217
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| 摘要: |
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 → ∞.
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- 15/1/2008
| 題目: |
Response-Adaptive Designs and Their Applications |
| 講員: |
Dr. Feifang Hu, Department of Statistics, University of Virginia, USA |
| 時間/地點: |
11:30 - 12:30
FSC 1217
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| 摘要: |
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.
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- 23/1/2008
| 題目: |
A Robust High Resolution Solver for Steady Euler Equations on Unstructured Grids |
| 講員: |
Mr. Guanghui Hu, Department of Mathematics, Hong Kong Baptist University, Hong Kong |
| 時間/地點: |
10:30 - 11:30
FSC 1217
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| 摘要: |
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.
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- 23/1/2008
| 題目: |
Testing for Smoothing Spline Models: An Variance Component Testing Approach |
| 講員: |
Mr. Ziqing Chang, Department of Mathematics, Hong Kong Baptist University, Hong Kong |
| 時間/地點: |
14:30 - 15:30
FSC 1217
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| 摘要: |
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.
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- 23/1/2008
| 題目: |
Statistical Inference for the Correlated Data from Paired Organs |
| 講員: |
Ms. Yanbo Pei, Department of Mathematics, Hong Kong Baptist University, Hong Kong |
| 時間/地點: |
15:30 - 16:30
FSC 1217
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| 摘要: |
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.
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- 28/1/2008
| 題目: |
Artificial Boundary Method for Two-Dimensional Burgers Equation |
| 講員: |
Mr. Jiwei Zhang, Department of Mathematics, Hong Kong Baptist University, Hong Kong |
| 時間/地點: |
15:30 - 16:30
FSC 1217
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| 摘要: |
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.
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