关于举行邱兴教授短期讲学的通知

讲学标题：Statistical Methods for Differential Equation Modeling

报告人:邱兴教授 (罗彻斯特大学)

报告地点:四号楼 4318

邀请人：姚仰新教授

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讲课内容及时间安排：

                                                                                                                        数学学院

                                                                  2018年8月19日

Course Description

   We propose to study the statistical analysis on manifold by the method of symmetry. Many useful manifolds are symmetric under certain Lie group actions. These groups have a very nice property: due to the symmetry, a large part of the mathematical properties of a Lie group is characterized by the tangent space at its identity element (the Lie algebra). From the statistical perspective, if we have a statistical model that is invariant or equivariant under a Lie group transformation, we can first study the properties of the corresponding Lie algebra, which is a linear space therefore easy to study, and then use the exponential map to translate these properties back to the original Lie group hence the original statistical model. We can also use Lie groups to construct maximal invariant, and use it as an efficient dimension reduction method.

Course Aims and Objectives

   We will teach students hypothesis testing, parameter estimation and dimension reduction technique from the geometric perspective, so that they have a geometric thinking in statistical research. Specifically, we will formally define symmetry (invariance and equivariance) for statistical models, and use my recent research projects to explain the utility of symmetry in statistical research. The students are also expected to master statistical, mathematical, and computational skills that are necessary for their future research.

Course Policies and Expectations

    Students are expected to attend every class and finish homework and/or projects in a timely fashion. Students may bring laptops to class to assist learning.