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Taylor'sLaw of Fluctuation Scaling

发布日期:2019-06-10     作者:数学学院      编辑:王馨霖     点击:

报告题目:Taylor'sLaw of Fluctuation Scaling

报 告 人:Joel E. Cohen教授 洛克菲勒大学和哥伦比亚大学 美国科学院院士

报告时间:2019年7月10日上午9:00-10:00

报告地点:数学楼一楼第一报告厅

报告摘要:

A family of nonnegative random variables parameterized by θis said to obey Taylor's law when the variance is proportional to some power ofthe mean: for each θ in some set, the random variable labeled by θ obeysvariance(θ) ≈ a×[mean(θ)]^b. Here "≈" may mean exact, approximate, orasymptotic equality. E.g., in the family of exponential distributions, eachparameterized by its mean μ∈(0,∞), the variance is μ^2 , so a=1, b=2. Thediscrete-time Galton-Watson branching process, the continuous-time linear birthand death process, and many other stochastic processes obey Taylor's law.Thousands of empirical illustrations of Taylor's law have been published inmany different fields including ecology, demography, finance (stock andcurrency trading), cancer biology, genetics, fisheries, forestry, meteorology,agriculture, physics, cell biology, computer network engineering, and numbertheory. This survey talk will review some empirical and theoretical results andopen problems with the goal of stimulating further theory and applications ofTaylor's law. I will describe recently proved versions of Taylor's law fornonnegative stable laws with infinite mean and for functions related to thevariance such as the upper and lower semivariance, which are used widely inagricultural economics and portfolio management.

报告人简介:

Joel E. Cohen是美国洛克菲勒大学的Abby Rockefeller Mauzé教授哥伦比亚大学的教授。他和他的同事使用数学,统计和计算工具研究人口,生态系统和环境。他的工作重点是影响人类健康的现象,人类与之相互作用的其他物种以及人类环境。最近的例子包括食物网,昆虫传播的感染,龙卷风和人口动态。Cohen使用模型来预测未来的人口增长,国际移民,生命以及教育与生育的相互作用。

Cohen教授在哈佛大学接受教育,并获得了学士学位。以优异成绩,获得两个硕士学位和两个博士学位,一个是应用数学,另一个是人口科学和热带公共卫生。他一直在哈佛大学任教,直到1975年,他加入洛克菲勒大学,担任教授和人口实验室负责人。此外,自1995年以来,他一直是哥伦比亚大学国际和公共事务学院的教授。他还隶属于哥伦比亚大学地球与环境科学系及统计系。他在芝加哥大学统计系有名誉任命。

他是美国国家科学院院士,美国艺术与科学学院院士,美国哲学学会会员。他获得过麦克阿瑟基金会奖学金,这一被称为“天才”的奖,以及古根海姆奖奖学金,日本科学促进会的奖学金。他分享了泰勒环境成就奖和华盛顿特区泛美卫生组织Fred L. Soper奖的成果,以供人们研究南美锥虫病。他曾在阿根廷,中国,英国,法国和日本担任名誉和访问学术任命。Cohen教授获得了人口委员会颁发的第一个Olivia Schieffelin Nordberg奖,以表彰他1995年出版的How Many People Can the Earth Support?他还编写或编辑了其他13本书,其中包括两本关于普及教育,一系列科学和数学笑话,绝对零重力以及430多篇科学论文和章节。

报告题目:Mixed model enrichmentanalysis of gene expression data

报 告 人:Duo Jiang教授 美国俄勒冈州立大学

报告时间:2019年7月10日上午10:20-11:00

报告地点:数学楼一楼第一报告厅

报告摘要:

Competitive gene-set analysis, also called enrichment analysis,is a widely used tool for interpreting high-throughput biological data such asgene expression data. It aims at testing a known category (e.g. a pathway) ofgenes for enriched differential expression (DE) signals compared to genes notin the category. Most conventional enrichment testing methods ignore the widespreadcorrelations among genes, which has been shown to result in excessive falsepositives. We evaluate, both methodologically and empirically, previous methodsto account for correlations, and show that they fail to accommodate the DEheterogeneity across genes and can result in severely mis-calibrated type Ierror and/or power loss. We propose a new framework, MEACA, for gene-settesting based on a mixed effects quasi-likelihood model. Our method flexiblyincorporates the unknown distribution of DE effects, and effectively adjustsfor completely unknown, unstructured correlations among genes. Compared toexisting methods such as GSEA and CAMERA, MEACA enjoys robust and substantiallyimproved control over type I error and maintains good power in a variety ofcorrelation structure and differential expression settings. We also present tworeal data analyses to illustrate the advantage of our approach.

报告人简介:

Duo Jiang是美国俄勒冈州立大学的助理教授。她于2014年获得了芝加哥大学的统计学博士学位,在此之前她获得了清华大学的学士学位。她的研究重点是开发遗传学和基因组学数据的统计方法。最近的一些项目涉及微生物组数据分析,基因表达数据的富集分析以及多组学数据整合。



报告题目:Hierarchical Community Detection withFiedler Vectors

报 告 人:Xiaodong Li教授美国加州大学戴维斯分校

报告时间:2019年7月10日上午11:00-11:40

报告地点:数学楼一楼第一报告厅

报告摘要:

Hierarchicalclustering of entities based on observations of their connections has alreadybeen widely studied and implemented in the practice of network analysis.However, the statistical properties of diverse hierarchical community detectionare still majorly unclear. We here propose to extend the binary tree stochasticblock model in the literature to accommodate much more general compositions ofedge probabilities. It can be shown that the eigen-structures of the graphLaplacian of the population binary tree stochastic block model reveals thelatent structure of the network at all levels. This fact inspires us toretrieve the hidden hierarchical structure of communities by using a recursivebi-partitioning algorithm with Fiedler vector, dividing a network into twocommunities repeatedly until a stopping rule indicates there are no furthercommunities. The method is further theoretically justified in sparse networkswith the help of the newly developed theory about entry-wise bound foreigenvector perturbations. The is based on an ongoing project with my studentXingmei Lou.

报告人简介:

Xiaodong Li博士是美国加州大学戴维斯分校统计系助理教授。在此之前,他曾在美国宾夕法尼亚大学沃顿商学院统计系工作了两年。他于2013年获得美国斯坦福大学数学博士学位,并于2008年获得北京大学学士学位。他对网络分析,无监督学习理论和数学信号处理有着广泛的研究兴趣。他的论文发表在各种统计学,数学和工程学期刊上,如AoS,ACHA,FOCM,JACM,IEEE TIT等等。



报告题目:GeneralizedAdditive Coefficient Models with High-dimensional Covariates for GWAS

报 告 人:Hua Liang教授 美国乔治华盛顿大学

报告时间:2019年7月10日下午1:30-2:10

报告地点:数学楼一楼第一报告厅

报告摘要:

In thelow-dimensional case, the generalized additive coefficient model (GACM)proposedhas been demonstrated to be a powerful tool for studying nonlinearinteractioneffects of variables. In this paper, we propose estimation andinferenceprocedures for the GACM when the dimension of the variables is high.Specifically,we propose a group-wise penalization based procedure to distinguishsignificantcovariates for the large p small n setting. The procedure is shown to beconsistent for model structure identification. Furthermore, we construct simultaneousconfidence bands for the coefficient functions in the selected modelbasedon a refined two-step spline estimator. We also discuss how to choosethetuning parameters. To estimate the standard deviation of the functionalestimator,we adopt the smoothed bootstrap method. We conduct simulationexperimentsto evaluate the numerical performance of the proposed methods and analyze anobesity data set from a genome-wide association study as an illustration.

报告人简介:

Hua Liang是美国乔治华盛顿大学统计系统计和生物统计学教授(2013 ---至今)。Liang教授于1992年获得中国科学院系统科学研究所数学统计学博士学位,并于2001年获得美国德州农机大学统计学博士学位。他是St. Jude儿童研究医院的助理教授(2002-2005),罗切斯特大学医学中心的副教授(2005-2009)和教授(2009-2013)。Liang教授致力于半参数回归,纵向数据的混合效应模型,缺失数据,测量误差模型,变量选择和HIV动态模型等方向的研究。他获得了两项美国国立卫生研究院的RO1,一项T32和五项NSF研究经费。他是美国统计协会,国际数理统计协会,皇家统计学会会员和国际统计协会的当选会员。Biometrics, Electronic Journal of Statistics和JASA的副主编



报告题目:Identification ofrhythmic signals in oscillatory systems with applications to chronobiology

报 告 人:Shyamal Peddada教授 美国匹兹堡大学

报告时间:2019年7月10日下午2:10-2:50

报告地点:数学楼一楼第一报告厅

报告摘要:

There is a growing interest in studying oscillatory systems in awide range of applications. For example, in pharmacology researchers areinterested in understanding circadian clock and estimating the time to peakexpression of circadian genes as they may play a critical role in determiningoptimal time of treatment. Astrophysicists are interested in identifyingtemporal patterns in the light emitted by stars to classify stars into groups,and so on. In each of these cases, the fundamental and challengingquestion of interest is to identify components in the oscillatory system thatdisplay a rhythmic pattern. In this talk we describe a very simple and yet avery general framework using constrained statistical inference basedmethods. The resulting methodology is robust to the shape of the pattern,thus the method does not limit to cosine type curves. The resulting methodologyis applied to some well-known circadian clock data.

报告人简介:

Shyamal Peddada自2017年起担任美国匹兹堡大学公共卫生院生物统计系教授和系主任。他于1983年在美国匹兹堡大学数学系获得博士学位,在C. R. Rao教授的指导下。在此之前,他是美国国立卫生研究院NIEHS生物统计学和计算生物学分部的高级研究员。Peddada教授为约束统计推断(参数和非参数),分析微生物组数据和基因表达研究的方法学做出了重要贡献。他还在各个科学领域做出了重要贡献,如女性肌瘤的生长,毒理学和毒理基因组学,婴儿和母体肠道微生物组和表观遗传学。他开发的软件包,用于分析微生物组数据的ANCOM和基因表达研究的ORIOGEN,被研究人员广泛使用。Peddada教授是美国统计协会杰出统计应用奖的获得者。他是美国统计协会和国际统计协会的当选会员。他曾担任JASA的副主编。



报告题目:UncertaintyQuantification of Treatment Regime in Precision Medicine with an Application inNonparametric Adaptive Design

报 告 人:Min-ge Xie教授 美国罗格斯大学

报告时间:2019年7月10日下午3:10-3:50

报告地点:数学楼一楼第一报告厅

报告摘要:

Personalized decisionrule in precision medicine is a `discrete parameter’, for which theoretical developmentof statistical inference is lacking. This talk proposes a new way to quantifythe estimation uncertainty in a personalized decision based on confidencedistribution (CD). Suppose, in a regression setup, the optimal decision fortreatment versus control for an individual z is determined by a linear decisionrule D = I(m_1(z))>m_0(z)), where m_1(z) and m_0(z) are the expectations ofpotential outcomes of treatment and control, respectively. The estimated D hasuncertainty. We propose to find a CD for v = m_1(z) – m_0(z) and compute a`confidence measure’ of the decision {D=1} = {v > 0}. This measure, withvalue in [0,1], provides a frequency-based assessment about the decision. Forexample, if the measure for {D=1} is 63%, then, out of 100 patients the same aspatient z, 63 will benefit using treatment and 37 will be better off in controlgroup. This confidence measure is shown to match well with the classical assessmentsof sensitivity and specificity, but without the need to know the true {D=1} or{D=0}. Utility of the development is demonstrated in an adaptive clinical trialwith nonparametric regression models. Joint work with Yilei Zhan (RutgersUniversity) and Sijian Wang (Rutgers University)

报告人简介:

Min-ge Xie是美国罗格斯大学统计系的杰出教授,同时也是美国罗格斯大学统计咨询办公室的主任。他的主要研究兴趣在于弥合统计推断的基础,并为跨学科研究产生的问题开发新的统计方法和理论。他的研究兴趣还包括生物医学科学,社会科学,工业,工程和环境科学的统计应用。他获得过中国科学技术大学(USTC)的数学学士学位和伊利诺伊大学厄巴纳-香槟分校(UIUC)的统计学硕士和博士学位。他曾参与过由国家科学基金会(NSF),国家卫生研究院(NIH),退伍军人事务部(VA),联邦航空管理局等机构资助的研究项目。



报告题目:Simultaneous Prediction intervals for high-dimensional VectorAutoregressive model

报 告 人:Mengyu Xu教授美国中佛罗里达大学

报告时间:2019年7月10日下午3:50-4:30

报告地点:数学楼一楼第一报告厅

报告摘要:

We study the simultaneous predictionintervals for high-dimensional vector autoregressive model. We consider ade-biased calibration for the lasso prediction and propose aGaussian-multiplier bootstrap based method for one-step ahead prediction. Theasymptotic coverage consistency of the prediction interval is obtained. We alsodevelop simulation result to evaluate the finite sample performance of theprocedure.

报告人简介:

Mengyu Xu于2010年获得中国人民大学统计学学士学位。她分别于2012年和2016年在美国芝加哥大学芝加哥大学统计系获得硕士和博士学位。她目前是美国奥兰多中佛罗里达大学统计系的助理教授。她的研究兴趣包括协方差矩阵估计和高维时间序列的网络恢复以及二次型和高维假设检验的分布理论。

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