Event(s) on June 2018

• Wednesday, 6th June, 2018

  Title:	Inverse Source Problems for Wave Propagation
  Speaker:	Professor Peijun Li, Department of Mathematics, Purdue University, Indiana, USA
  Time/Place:	10:00  -  11:00 FSC703, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	The inverse source problems, as an important research subject in inverse scattering theory, have significant applications in diverse scientific and industrial areas such as antenna design and synthesis, medical imaging, optical tomography, and fluorescence microscopy. Although they have been extensively studied by many researchers, some of the fundamental questions, such as uniqueness, stability, and uncertainty quantification, still remain to be answered.  In this talk, our recent progress will be discussed on the inverse source problems for acoustic, elastic, and electromagnetic waves. I will present a new approach to solve the stochastic inverse source problem. The stability will be addressed for the deterministic counterparts of the inverse source problems. We show that the increasing stability can be achieved by using the Dirichlet boundary data at multiple frequencies. I will also highlight ongoing projects in random medium and time-domain inverse problems.

  
  

• Thursday, 7th June, 2018

  Title:	Fast algorithms for multi-particle scattering and its inverse problem
  Speaker:	Dr Jun Lai, School of Mathematical Sciences, Zhejiang University , Hangzhou, China
  Time/Place:	09:30  -  10:30 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	Electromagnetic scattering in multiple particles appears in a lot of applications, including biophysics, solar cell and metamaterial design. Given the property of a single particle, it is often desirable to obtain a composite material with a given electromagnetic response, in which fast algorithm is needed. In this talk, I will talk about numerical algorithms based on integral equations and fast multipole method to rapidly find the scattering of multiple particles in various medium, including layered medium and periodic medium, as well as the extension to elastic scattering of multiple particles. I will also discuss some recent work on the inverse scattering problem for multiple particles and three dimensional scattering from axis-symmetric objects.

  
  

• Tuesday, 19th June, 2018

  Title:	Automatic Shape-constrained Nonparametric Regression
  Speaker:	Prof Huixia Wang, Department of Statistics, George Washington University, Washington, USA
  Time/Place:	10:00  -  11:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	Shape information such as monotonicity and convexity of regression functions, if available, can be incorporated in nonparametric regression to improve estimation accuracy. However, in practice, the functional shapes are not always known in advance. On the other hand, using hypothesis testing to determine shapes would require testing various null and alternative hypotheses, and thus is not practical when interests are on many functional curves. To overcome this challenge, we propose a new penalization-based method, which provides function estimation and automatic shape identification simultaneously. The method estimates the functional curve through quadratic B-spline approximation, and captures the shape feature by penalizing the positive and negative parts of the first two derivatives of the spline function in a group manner. Under some regularity conditions, we show that the proposed method can identify the correct shape with probability approaching one, and the resulting nonparametric estimator can achieve the optimal convergence rate. Simulation shows that the proposed method gives more stable curve estimation and more accurate shape identification than the unconstrained B-spline estimator, and it is competitive to the shape-constrained estimator assuming prior knowledge of the functional shape. The proposed method is applied to a motivating vocalization study to examine the effect of Mecp2 gene on the vocalizations of mice during courtship.

  
  

• Tuesday, 19th June, 2018

  Title:	Variance change point detection under a smoothly-changing mean trend with application to liver procurement
  Speaker:	Prof Pang Du, Department of Statistics, Virginia Tech University, United States
  Time/Place:	11:00  -  12:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	Literature on change point analysis mostly require a sudden change in the data distribution, either in a few parameters or the distribution as a whole. We are interested in the scenario where the variance of data may make a significant jump while the mean changes in a smooth fashion. The motivation is a liver procurement experiment monitoring organ surface temperature. Blindly applying the existing methods to the example can yield erroneous change point estimates since the smoothly-changing mean violates the sudden-change assumption. We propose a penalized weighted least squares approach with an iterative estimation procedure that integrates variance change point detection and smooth mean function estimation. The procedure starts with a consistent initial mean estimate ignoring the variance heterogeneity. Given the variance components the mean function is estimated by smoothing splines as the minimizer of the penalized weighted least squares. Given the mean function, we propose a likelihood ratio test statistic for identifying the variance change point. The null distribution of the test statistic is derived together with the rates of convergence of all the parameter estimates. Simulations show excellent performance of the proposed method. Application analysis offers numerical support to non-invasive organ viability assessment by surface temperature monitoring. This is joint work with Zhenguo Gao, Zuofeng Shang, and John Robertson.

  
  

• Thursday, 21st June, 2018

  Title:	Estimation and classification for varying-coefficient panel data model with latent structures
  Speaker:	Dr Tao Huang, School of Statistics and Management, Shanghai University of Economics and Finance, Shanghai, China
  Time/Place:	10:30  -  11:30 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	A varying coefficient panel data model with unknown group structures is considered, where the group membership of each individual and the number of groups are left unspecified. We first develop a triple localization approach to estimate the unknown coefficient functions, and then identify latent grouped structures via community detection method. To improve the efficiency of the resultant estimator, we further propose a two-stage estimation method that enables the resulting estimator achieve optimal rates of convergence. In the theoretical part of the paper, the asymptotic theory of the resultant estimators are derived. In particular, we provide the convergence rates and the asymptotic distribution of our estimators. In the empirical part, several simulated examples and a real data analysis are presented to illustrate the finite sample performance of the proposed methods.

  
  

• Friday, 22nd June, 2018

  Title:	Optimal and Data-Adaptive P-value Combination Tests For Correlated Data
  Speaker:	Prof Zheyang Wu, Department of Mathematical Sciences, Worcester Polytechnic Institute, United States
  Time/Place:	11:00  -  12:00 FSC1111, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	P-value combination is an important statistical approach for information-aggregated decision making. It is foundational to a lot of applications such as meta-analysis, data integration, signal detection, and others. We propose two generic statistic families for combining p-values: gGOF, a general family of goodness-of-fit type statistics, and tFisher, a family of Fisher type p-value combination with a general weighting-and-truncation scheme. The two families unify many optimal statistics over a wide spectrum of signal patterns. Within these two families of statistics, data-adaptive omnibus tests are also designed for adapting the family-retained advantages to unknown signal patterns. For analyzing correlated data, we provide efficient solutions for analytical calculations of the p-value. We reveal the influence of data transformations to the signal-to-noise ratio and the statistical power under the Gaussian mean model and the generalized linear model. Applications of these methods are illustrated in gene-based SNP-set studies of genetic associations.

  
  

• Monday, 25th June, 2018

  Title:	Multiple change point detection for manifold-valued data with applications to dynamic functional connectivity
  Speaker:	Prof Qiang Sun, Department of Statistical Sciences & Department of Computer and Mathematical Sciences , University of Toronto, Toronto, Canada
  Time/Place:	10:30  -  11:30 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	In neuroscience, functional connectivity describes the connectivity between brain regions that share functional properties. It is often characterized by a time series of covariance matrices between functional measurements of distributed neuron areas. An elective statistical model for functional connectivity and its changes over time is critical for better understanding neurological diseases. To this end, we propose a log-mean model with an additive heterogeneous noise for modeling random symmetric positive definite matrices that lie in a Riemannian manifold. We introduce the heterogeneous error terms to capture the curved nature of the manifold. A scan statistic is then developed for the purpose of multiple change point detection. Despite that the proposed model is linear and additive, it is able to account for the curved nature of the Riemannian manifold. Theoretically, we establish the sure coverage property. Simulation studies and an application to the Human Connectome Project lend further support to the proposed methodology.

  
  

• Monday, 25th June, 2018

  Title:	Modelling the customer lifetime value with a zero-adjusted inverse Gaussian model
  Speaker:	Prof Meko So, Department of Decision Analytics and Risk, Southampton Business School, United Kingdom
  Time/Place:	16:30  -  17:30 AAB503, Academic and Administration Building, Baptist University Road Campus, Hong Kong Baptist University
  Abstract:	Estimating the customer lifetime value (CLV) is one of the important topics for marketers. CLV is commonly used as a key measure to categorise customers into groups and thus having an accurate estimation could help companies in deciding how much marketing resources to allocate to different groups of customers. This paper aims to develop an empirical approach to estimate the CLVs of ferry customers. With a mix of tourists who travel relatively infrequently and regular customers, we introduce the use of a zero-adjusted inverse Gaussian (ZAIG) to model the large mass of customers who will not return at all. Through working with the ferry company Red Funnel, we use a large customer transaction dataset to test the performance of our model.

  
  

• Tuesday, 26th June, 2018

  Title:	A Fixed Mesh Method With Immersed Finite Elements for Solving Interface Inverse Problems
  Speaker:	Dr Ruchi Guo, Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia
  Time/Place:	16:30  -  17:30 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	In this talk, I will present a new fixed mesh algorithm for solving a class of interface inverse problems for the typical elliptic interface problems. These interface inverse problems are formulated as shape optimization problems whose objective functionals depend on the interface shape. Both the governing partial differential equations and objective functionals are discretized optimally by an immersed finite element (IFE) method on a fixed mesh independent of interface location. The formula for the shape sensitivities of the discretized objective functions is derived within the IFE framework that can be computed accurately and efficiently through the discretized adjoint method. We show its applications to a group of representative interface inverse/design problems.

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