统计与应用数学研讨会

Semiparametric Methods for Survival Data with Measurement Error under Additive Hazards 治愈率模型

Abstract: It is well established that measurement error has drastically negative impact 十大彩票网投平台数据分析. 它不仅会对参数估计产生偏差，还可能造成损失 检验变量间关系的幂. 尽管生存分析 error-contaminated data has attracted extensive interest, relatively little attention has been paid to dealing with survival data with error-contaminated covariates when 潜在人群的特征是治愈部分. 在本文中，我们 consider this problem for which lifetimes of the non-cured individuals are featured by the additive hazards model and the measurement error process is described by an 加性模型. 与比例风险模型中的相对风险估算不同， the additive hazards model allows us to estimate the absolute risk difference associated 用协变量. 为了允许模型的灵活性，我们加入了与时间相关的 模型中的协变量. 我们为这两种情况开发了评估方法，没有 或者测量误差. 从理论上对所提出的方法进行了评价 视角和数值视角.

From Statistical Process Control (SPC) to Machine Learning and Fundamental Assisted 分析(FAA):钢铁工业的转型

Abstract: With over a billion ton plus global production, Steel is often considered as one of the most important manufacturing industries which involves many industrial 这是资本和操作成本密集的过程. SPC一直是不可或缺的 part of the quality control aspects for various steel plants, and therefore, steel 工厂已经投入大量资金使用SPC方法来改进他们的工艺. 用这个 in mind, the steel industry progressed steadily into the 1990s when steel-makers got interested in dynamic process control and Artificial Neural Network based dynamic 基于工厂数据的模型. 2010年，大数据成为钢铁业的下一个热词 米尔斯. 尽管听起来很好，但钢铁厂的数据离“大数据”还差得远。 与社交网络和营销数据量相比. 自2016年起， the buzz of artificial intelligence and machine learning became popular, and many 设备供应商和顾问开始开发智能机器. 他们 claimed that such efforts would enable process control through real time analytics 这些机器和整个钢铁厂都会“自我学习”. 在回顾 the reality of these claims, it was often observed that static models developed in the 1980s were being recycled with a fancier graphical user interfaces and named ‘intelligent’. The use of AI and ML based systems was not readily appreciated or adopted by steel makers, and instead people still believed in the fundamentals of metallurgy and steelmaking. Currently, steel makers are waiting for the next generation of SPC based on fundamentals 辅助分析将在全球范围内主导未来的钢铁制造.

十大彩票网投平台动力系统不变环面的持久性

Abstract: 给n a dynamical system (in finite or infinite dimension) it is very natural to look for finite dimensional invariant subspaces on which the dynamics is very simple. Of particular interest are the invariant tori on which the dynamics is conjugated 变成线性的. 这类物体在扰动下的持续性问题 been widely studied starting form the 50's, and this gives rise to the celebrated 锦理论. 这次谈话的目的是对主要的困难和困难进行概述 策略，考虑到PDE的应用.

骨重塑的动力系统方法

Abstract: Bone remodeling is a lifelong process where mature bone tissue is removed 从骨骼和新的骨组织形成. 这些过程也控制着 reshaping or replacement of bone following injuries like fractures but also micro-damage, 在正常活动中会发生什么. 我们讨论了二和的适当的一般类 three-dimensional population models for the cell types involved in this process and 证明两个种群不足以解释生物学家所观察到的. 一个三维的 model class not only explains the observations but also explains what is called Paget's 骨重塑紊乱的疾病. 数学工具是 developed step by step and describe the basics of a 'bifurcation theory for an infinity 具有相同耦合结构的常微分方程个数. 这 是与Thilo Gross, Martin Zumsande和Dirk Stiefs的合作作品吗.

Canards, Mixed-Mode Oscillations and Chaos in a Two-Trophic Ecological Model: Sensitivity 参数和环境波动

Abstract: We consider a two-trophic ecological model comprising of two predators competing 同样的猎物. 假设猎物的生长速度要大得多 than that of the predators, the problem is viewed as a singular perturbed system in 一个快变量和两个慢变量. 我们假设其中一个掠食者(领地) 死亡率与密度有关. 在无非领土的情况下 predator, the subsystem exhibits a canard explosion, which refers to a change from an outbreak dynamics to small oscillations around the two species equilibrium state 在极短的时间间隔内. 领地捕食者的死亡率 是多样的，全系统表现出各种丰富的动态，包括但不包括 limited to relaxation oscillations (which represent periodic outbreaks interspersed with collapses of the populations), mixed-mode oscillations (which are concatenations of small amplitude and large amplitude oscillations) that indicate the adaptability 延长繁荣与萧条的周期，以及混乱. 数值模拟 are carried out to demonstrate the sensitivity of the system to initial 条件 和参数. 最后，如果时间允许，我们将简要讨论……的影响 系统上的“噪音”.

k维ROC流形的假设检验

Abstract: Consider any classification procedure for K groups based on a certain marker X. Let; X_i ~ F_i; i = 1, 2, ...， K，其中F_i 是连续的， ...,K. 最常用的衡量性能的指标 of the marker is HUM (Hyper-volume Under Manifold) of the ROC (Receiver Operating 特征)由该标记获得的流形. 随机标记获得的HUM值为 1/K!. 因此，测试标记性能的自然设置是H₀: hum = 1/ k! vs. H_A: HUM > 1/K!. However, for even moderately large K; this test is useless as 1/K! 是收敛的 to 0. 我将讨论两个用于测试K上的标记性能的新测试 (> 2) group classification problem.

不可忽略缺失响应的基于等级的推理

摘要:数据采集过程中经常会出现观测缺失现象. 的机制 导致缺失的特征是其随机性程度. 在这个 talk, the focus is placed on observations that have missing responses in the context 回归建模. 这种缺失被认为不是随机的——也被认为是已知的 作为不可忽略. 回归模型参数估计的现有方法 when data contain outliers or in presence of errors distributions that are heavy tailed, 提供效率低下和/或不健壮的估计. 我们建议以等级为基础 approach to estimating the true regression parameters with the missing responses being imputed via either a simple imputation or an inverse marginal probability imputation. The imputation methods are then incorporated in the regression model leading to a robust rank-based estimate of the parameters via the considered objective function. Large sample properties of the proposed estimator are established under mild regularity 条件. 进行了蒙特卡罗仿真实验，证明了基于秩的方法 estimator is more efficient than the least squares estimator whenever the error distribution 是重尾还是受污染，处于不可忽视的反应状态. 最后，举个例子 讨论了实例.