饮酒后血液中乙醇含量的推断

基于采集的32名健康志愿者饮酒后血液中乙醇含量(BAC)随时间变化的数据,共128个数据.首先运用纵向数据分析方法中的随机效应混合模型进行分析,结果显示可以比较精确的预测BAC,模型的绝对平均误差(MAE)为1.18mg/100ml、绝对误差的中位数为0.89mg/100ml.其次对数据不作任何分布假设,运用机器学习回归方法分析数据,最后利用10折交叉验证方法来判断结果的可靠性,并得到各模型测试集的标准化均方误差(NMSE)分别为0.012,0.003,0.803,0.761,0.853.     

具有AR(1)误差的非线性随机效应模型中自相关系数的扰动诊断

随机效应模型广泛应用于刻画重复测量数据的特征,Banerjee和Frees[1]用Cook距离,Lesaffre和Verbeke[2]用影响曲率分别对线性随机效应模型进行了分析.本文利用影响曲率对具有AR(1)误差的非线性随机效应模型中的自相关系数扰动进行了分析,得到了影响曲率的表达式,并且利用血浆药物渗透数据(Davidian和Gillinan[3])来说明分析方法的应用.     

混合效应模型及其在非寿险费率厘定中的应用

在非寿险分类费率厘定中,广义线性模型的应用十分普遍,但当某些费率因子的水平数很多时(本文称之为多水平因子),广义线性模型的估计结果将不可靠。解决此类问题的一种方法是把多水平费率因子作为随机效应处理。将多水平费率因子作为随机效应处理可以采取下述三种方法:(1)分别用广义线性模型和信度模型估计普通费率因子和多水平因子,通过广义线性模型与Buhlmann-Straub信度模型的迭代应用预测索赔频率和索赔强度;(2)应用广义线性混合模型分别预测索赔频率和索赔强度;(3)直接对经验纯保费数据建立Tweedie混合效应模型。本文把上述模型应用于中国车损险实际数据的研究结果表明,这三种方法比较接近,但从总体上看,广义线性混合模型的估计结果更加可取。     

城市道路短时交通流量预测

结合BP神经网络模型和自回归求和滑动平均(ARIMA)模型对城市道路交通短时区间流量进行预测.影响交通流的因素有很多,难以一一量化,但这些因素都可以由线性自相关结构和非线性结构结合线性组合得到.而BP神经网络对非线性关系有很好的拟合效果,ARIMA模型则具有良好的线性拟合能力.在训练模型时,先用ARIMA模型拟合训练集,与原始数据作差得到一组残差;用BP神经网络模型拟合残差;将两个模型结合得到组合模型.将2017年7月1日7:00到2017年7月1日18:00期间,贵阳市某个路口断面所采集的过车数据作为训练集,建立ARIMA模型和BP神经网络模型以及组合模型,预测2017年7月1日18:00到2017年7月1日19:00的短时交通流.过车数据统计时间间隔为5min,则训练集共有有效数据132组,测试集的有效数据为12组.分别用三类误差分析指标比较三个模型的拟合、预测效果,结果显示组合模型的预测效果比两个模型单独使用的预测效果更准确.     

非线性再生散度随机效应模型的贝叶斯分析

非线性再生散度随机效应模型是一类非常广泛的统计模型，包括了线性随机效应模型、非线性随机效应模型、广义线性随机效应模型和指数族非线性随机效应模型等．本文研究非线性再生散度随机效应模型的贝叶斯分析．通过视随机效应为缺失数据以及应用结合Gibbs抽样技术和Metropolis-Hastings算法（简称MH算法）的混合算法获得了模型参数与随机效应的同时贝叶斯估计．最后，用一个模拟研究和一个实际例子说明上述算法的可行眭．     

线性混合模型用于艾滋病疗效预测和疗法选优

为探究线性混合效应模型在艾滋病疗效预测和疗法选优中的应用。利用美国艾滋病医疗试验机构ACTG的193A研究中的一组非平衡重复测量数据,以logcd4为体现疗效的因变量,年龄、性别为固定效应,建立截距和治疗时间的斜率随受试者随机变化且其期望值因疗法不同的线性混合效应模型,用SAS软件中mixed过程求解并预测。通过疗法对截距和治疗时间斜率期望值的影响选择最优疗法。结果表明模型有非常好的拟合和预测效果,疗法4为最优疗法。本研究为专业医生进行艾滋病疗效的预测和疗法选优提供了科学依据和方法。     

收敛性随机森林模型及其遥感应用

通过引入全局损失函数,提出了一种全局优化的随机森林模型算法,称为θ-β型随机森林,并且利用改进后的模型对城市遥感图进行了检测与识别,识别准确率与识别速率都得到了一定的提高.方法在经典随机森林模型的基础上加入前向反馈模型(Forward Stagewise Additive Model),通过每一层节点的训练结果干预下一层的训练数据(从而改变阈值θ的选择)与训练步长(β),使得最后训练得到的型随机森林收敛速度更快,预测结果更为准确.     

基于纵向数据与生存时间数据联合建模的变量选择

纵向数据和生存时间数据联合建模能减少由单独建模所引起的偏差,本文研究了基于纵向数据和生存时间联合建模的变量选择问题。对于生存时间数据,把生存时间做离散化处理,引入离散风险函数的Probit模型;对于纵向数据,利用线性混合效应模型建模。采用共享随机效应的方法对纵向数据和生存时间进行联合建模,通过利用多元高斯隐截断分布,构造出联合模型的精确似然。然后对似然函数加惩罚,重新构造目标函数,得到回归系数的稀疏估计量。理论证明以及数值模拟研究展示了稀疏估计量的良好性质。     

拟自适应分类随机森林算法

本文给出了集成学习模型可以收敛的集成学习算法,拟自适应分类随机森林算法。拟自适应分类随机森林算法综合了Adaboost算法和随机森林算法的优势,实验数据分析表明,训练集较大时,拟自适应随机森林算法的效果会好于随机森林算法。另外,拟自适应分类随机森林算法的收敛性确保它的推广误差可以通过训练集估计,所以,对于实际数据,拟自适应分类随机森林算法不需要把数据划分为训练集和测试集,从而,可以有效的利用数据信息。     

指数族非线性混合效应模型基于$Q$函数的数据删除度量

对指数族非线性混合效应模型, 本文基于$Q$函数(朱宏图, 2001)方法, 给出几种度量数据删除影响的统计量\bd 其主要思想是将随机效应视为缺失数据, 并利用EM算法来处理完全数据对数似然函数的条件期望\bd 一个实际例子说明我们方法是有效的     

Robust portfolio selection based on asymmetric measures of variability of stock returns

This paper addresses a new uncertainty set—interval random uncertainty set for robust optimization. The form of interval random uncertainty set makes it suitable for capturing the downside and upside deviations of real-world data. These deviation measures capture distributional asymmetry and lead to better optimization results. We also apply our interval random chance-constrained programming to robust mean-variance portfolio selection under interval random uncertainty sets in the elements of mean vector and covariance matrix. Numerical experiments with real market data indicate that our approach results in better portfolio performance.     

随机事件与随机变量概率分布的拓展研究

给出了随机事元的拓展概率以及随机事元可拓集的概念.运用可拓集合、可拓变换与可拓推理等可拓学的理论与方法,对随机事件发生的概率与随机变量概率分布的变化作了初步的拓展研究.     

Time response of structure with interval and random parameters using a new hybrid uncertain analysis method

Practical structures often operate with some degree of uncertainties, and the uncertainties are often modelled as random parameters or interval parameters. For realistic predictions of the structures behaviour and performance, structure models should account for these uncertainties. This paper deals with time responses of engineering structures in the presence of random and/or interval uncertainties. Three uncertain structure models are introduced. The first one is random uncertain structure model with only random variables. The generalized polynomial chaos (PC) theory is applied to solve the random uncertain structure model. The second one is interval uncertain structure model with only interval variables. The Legendre metamodel (LM) method is presented to solve the interval uncertain structure model. The LM is based on Legendre polynomial expansion. The third one is hybrid uncertain structure model with both random and interval variables. The polynomial-chaos-Legendre-metamodel (PCLM) method is presented to solve the hybrid uncertain structure model. The PCLM is a combination of PC and LM. Three engineering examples are employed to demonstrate the effectiveness of the proposed methods. The uncertainties resulting from geometrical size, material properties or external loads are studied.     

在模糊随机因素影响下的多层圆筒结构的稳态热传导问题的区间数解法

在多层圆筒结构稳态热传导分析中,根据给定固体壁两侧表面温度总传热量公式,首先推导出当边界温度为随机变量情况下总传热量函数统计参数的均值和方差;然后推导出在导热系数为模糊数,边界温度为随机数下的总传热量的区间表达式．通过比较可以知道由区间数算法得到的区间最大,由概率统计算法得到的区间最小．并给出了两者的相对误差公式．最后引进粗糙集中的上、下近似集,提出用一个参数来统一定义模糊和随机区间进行稳态结构的热传导分析．     

模糊随机有限元平衡方程的摄动解法*

对模糊随机有限元平衡方程作λ水平截集,得随机区间平衡方程,然后基于平衡方程中有关力学量之间的关系,将随机区间平衡方程转化为两类普通随机平衡方程求解,利用小参数摄动理论导得求随机区间位移的递归方程组.文中还详细推导了计算模糊随机位移、模糊随机应变和模糊随机应力数字特征的计算公式.     

Transient landing dynamics analysis for a lunar lander with random and interval fields

This paper presents an objective comparison of random fields and interval fields to propagate spatial uncertainty, based on a finite element model of a lunar lander. The impulse based substructuring method is used to improve the analysis efficiency. The spatially uncertain input parameters are modeled by both random fields and interval fields. The objective of this work is to compare the applicability of both approaches in an early design stage under scarce information regarding the occurring spatial parameter variability. Focus is on the definition of the input side of the problem under this scarce knowledge, as well as the interpretation of the analysis outcome. To obtain an objective comparison between both approaches, the gradients in the interval field are tuned towards the gradients present in the random field. The result shows a very similar dependence and correlation structure between the local properties for both approaches. Furthermore, through the transient dynamic estimation, it is shown that the response ranges that are predicted by the interval field and random field are very close to each other.     

Modeling clustered binary data with nonparametric unobserved heterogeneity: An application to stock crash analysis

Various random effects models have been developed for clustered binary data; however, traditional approaches to these models generally rely heavily on the specification of a continuous random effect distribution such as Gaussian or beta distribution. In this article, we introduce a new model that incorporates nonparametric unobserved random effects on unit interval (0,1) into logistic regression multiplicatively with fixed effects. This new multiplicative model setup facilitates prediction of our nonparametric random effects and corresponding model interpretations. A distinctive feature of our approach is that a closed-form expression has been derived for the predictor of nonparametric random effects on unit interval (0,1) in terms of known covariates and responses. A quasi-likelihood approach has been developed in the estimation of our model. Our results are robust against random effects distributions from very discrete binary to continuous beta distributions. We illustrate our method by analyzing recent large stock crash data in China. The performance of our method is also evaluated through simulation studies.     

模糊数直觉模糊集运算的模糊结构元表示

在文[4]提出的模糊数直觉模糊集定义的基础上,将文[2]和[7]定义的区间值直觉模糊集运算推广到模糊数直觉模糊集中.利用模糊数的结构元表示方法,得到了模糊数直觉模糊集运算的简便的结构元表示形式,同时给出这些运算的相关性质及证明.     

Non-probabilistic convex models and interval analysis method for dynamic response of a beam with bounded uncertainty

This paper is concerned with the comparison of two non-probabilistic set-theoretical models for dynamic response measures of an infinitely long beam. The beam is on an uncertain foundation and subjected to a moving force with constant speed. The steady state vibration is analyzed with finite element method. The dynamic responses of the beam are approximated to the first-order respect of the uncertainty variables. As a rule, in convex models and interval analysis, the uncertainties are considered to be unknown, but they give out their allowable vector space. Comparing the convex models with interval analysis in mathematical proofs and numerical calculations, it’s shows that under the condition of transform an interval vector to an outer enclosed ellipsoid, the dynamic response of the infinitely long beam predicted by interval analysis is smaller than that by convex models; under the condition of transform a hyperellipsoid to an outer enclosed interval vector, the dynamic response of the infinitely long beam calculated by convex models is smaller than that by interval analysis method.     

Interval distribution function of a bounded chaotic sequence as a basis of nonaxiomatic probability theory

We introduce the notion of interval distribution function of random events on the set of elementary events and the notion of interval function of the frequencies of these events. In the limiting case, the interval function turns into the ordinary distribution function and the interval function of frequencies (under certain conditions) turns into the density of distribution of random events. The case of discrete sets of elementary events is also covered. This enables one to introduce the notion of the probability of occurrence of random events as a result of the limit transition. Translated From Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 8, Pp. 1128–1137, August, 2008.