统计学系系列讲座之302-304期

 

统计学系系列讲座之302

 

时间:2018年6月4日(周一)16:00-17:00

地点:史带楼503室

主持人:夏寅 青年研究员 复旦大学管理学院统计学系

主题:Statistical Problems in Brain Functional Connectivity Analysis

主讲人:Lexin Li Professor  Division of Biostatistics, University of California, Berkeley. 

简介:Lexin Li, 加州大学伯克利分校生物统计系教授,美国统计协会(American Statistical Association)会士。担任JASA, Technometrics等期刊副主编。研究领域包括神经影像数据分析、统计遗传学、降维、变量选择、机器学习、数据挖掘、计算统计等。

 

摘要:Brain functional connectivity maps the intrinsic functional architecture of the brain and reveals synchronization of brain systems through correlations in neurophysiological measures of brain activities. Accumulated evidences have suggested that it holds crucial insights of pathologies of a wide range of neurological disorders. Brain functional connectivity analysis is now at the foreground of neuroscience research, and is drawing increasing attention in the statistics field as well. A connectivity network is characterized by a graph, where nodes represent brain regions, and links represent statistical dependence that is often encoded by partial correlation. Such a graph is inferred from the matrix-valued neuroimaging data such as electroencephalography and functional magnetic resonance imaging. In this talk, we examine a number of statistical problems arising in brain connectivity analysis, including multi-graph penalized estimation, graph-based hypothesis testing, dynamic connectivity analysis, and dynamic network modeling. 

 

统计学系系列讲座之303

 

时间:2018年6月5日(周二)14:30-15:15

地点:史带楼301室

主持人:黎德元 教授  复旦大学管理学院统计学系

主题:Exploring Dependence in Multivariate Heavy Tailed Data

主讲人:Prof. Sidney I. Resnick  Cornell University, USA

 

摘要:Modeling multivariate heavy tailed data in d-dimensions using the usual semi-parametric regular variation assumption presents challenges due to the model being explicit only asymptotically. The definition requires estimating characteristics of a limit measure on d-space and the compactness of the support of the limit measure is one indicator of dependence among multivariate components. Identification of the support also allows the search for thinner tailed activity on the complement of the support. We have exploratory software which provides some assistance in the search for (a) the limit measure support; (b) the presence of additional thinner tailed regular variation behavior off the support; (c) the presence of subsets of variables being asymptotically independent. The identification of asymptotically independent sub-vectors is particularly important when identifying large risks unlikely to occur simultaneously while identifying thinner tailed regular variation off the support can improve risk estimation. Examples with both real and simulated data sets illustrate concepts; we consider social network data sets and stock returns from companies in similar sectors of the economy.

 

 

统计学系系列讲座之304

 

时间:2018年6月5日(周二)15:15-16:00

地点:史带楼301室

主持人:黎德元 教授  复旦大学管理学院统计学系

主题:Testing Independence of Random Elements with the Distance Covariance

主讲人:Prof. Thomas Mikosch  University of Copenhagen, Denmark

简介:T. Mikosch is professor for insurance mathematics at the University of Copenhagen. His main research interests are in applied probability, time series analysis, extreme value theory, and related statistical problems. T. Mikosch published more than 120 papers in peer reviewed journals and wrote 5 books. He is Editor of Extremes and Area Editor of Bernoulli. He is a foreign member of the Danish Royal Academy of Sciences and Letters and Elected Fellow of the IMS.

 

摘要:Distance covariance is a measure of dependence between vectors of possibly distinct dimensions. It has attracted attention in various fields of statistics and applied probability. We consider the distance covariance for stochastic processes X and Y defined on some interval and having square integrable paths, including Levy processes, fractional Brownian, diffusions, stable processes, and many more. Since distance covariance is defined for vectors we consider discrete approximations to X and Y. We show that sample versions of the discretized distance covariance converge to zero if and only if X and Y are independent. The sample distance covariance is a degenerate V-statistic and, therefore, has rate of convergence which is much faster than the classical root-n rates. This fact also shows nicely in simulation studies for independent X and Y in contrast to dependent X and Y.

 

                                                           统计学系 

2018-5-31