平方损失下屏蔽数据并联系统的经验贝叶斯分析

在部件寿命服从逆威布尔分布时,研究了屏蔽数据两部件并联系统的可靠性分析问题.基于截尾样本,将经典统计方法和贝叶斯理论相结合,推导出模型参数及系统可靠性指标的经验贝叶斯估计,最后给出数值模拟.     

基于动态因子结构的贝叶斯分位面板协整研究

针对传统面板协整检验在建模过程中易受异常值影响以及其原假设设置的主观选择问题,本文利用动态公共因子刻画面板数据潜在的截面相关结构,提出基于动态因子的截面相关结构的贝叶斯分位面板协整检验,结合各个主要分位数水平下参数的条件后验分布,设计结合卡尔曼滤波的Gibbs抽样算法,进行贝叶斯分位面板协整检验;并进行Monte Carlo仿真实验验证贝叶斯分位面板协整检验的可行性与有效性。同时,采用中国各省金融发展和经济增长的面板数据进行实证研究,结果发现在各主要分位数水平下中国金融发展和经济增长之间具有协整关系。研究结果表明:贝叶斯分位面板协整检验方法避免了传统面板数据协整方法由于原假设设置不同而发生误判的问题,克服了异常值的影响,能够提供全面准确的模型参数估计和协整检验结果。     

带有固定效应且n和T都很大的动态面板模型的诊断检验

研究了动态面板数据模型的诊断检验问题.对于带有固定个体效应且n和T都很大的的动态面板数据模型,通过残差的一阶差分构造了一个人工自回归模型,并基于该自回归模型系数的最小二乘估计构造了一个检验统计量检验模型的充分性.研究表明在一定的假设条件下,该检验渐近服从卡方分布,计算简单方便.模拟实验结果表明该检验表现很好.     

基于MCMC稳态模拟的指数回归模型及其应用

讨论了加速失效模型族中最简单而又十分重要的指数回归模型，利用贝叶斯方法提高了该模型的有效性。为了较好的解决高维数值积分在实际应用中的难题，提出了对寿命服从指数分布的产品，运用基于Gibbs抽样的马尔科夫链蒙特卡洛（Markov Chain Monte Carlo，MCMC）方法动态模拟出参数后验分布的马尔科夫链，在回归参数的先验分布为多元正态分布时，给出随机截尾条件下，回归参数在指数回归模型中的贝叶斯估计，提高了计算的精度。借助数据仿真分析说明了利用WinBUGS（Bayesian inference Using Gibbs Sampling）软件包进行建模分析的过程，证明了该模型在可靠性应用中的直观性与有效性。     

检验n和T都很大的固定效应动态面板模型的条件异方差性

研究了动态面板数据模型的条件异方差性检验问题.对于n和T都很大的固定效应动态面板数据模型,通过残差的一阶差分的平方序列,建立一个人工自回归模型,并基于该人工自回归模型系数的最小二乘估计构造检验统计量,检验误差序列的条件异方差性.研究表明在一定的假设条件下,得到的检验渐近服从卡方分布,计算简单方便,通过一些模拟试验研究了检验的小样本性质.模拟研究表明该检验表现很好.     

贝叶斯网络仿真元模型及其在装备战场损伤仿真中的应用研究

结合装备战场损伤仿真系统,研究了贝叶斯网络仿真元模型的构建方法.从条件概率角度描述了仿真模型输入参数与输出参数之间的映射关系,研究了构建贝叶斯网络仿真元模型的可行性,分析了贝叶斯网络仿真元模型的优点;研究了贝叶斯网络仿真元模型构建过程中的关键问题,包括:元模型参数的确定、原始模型参数向贝叶斯网络节点的转化、联结强度的计算、衍生元模型的构建;针对不完全信息条件下装备战场损伤快速定位问题,研究了基于K2算法的贝叶斯网络仿真元模型构建方法;构建了某型高炮的战场损伤贝叶斯网络仿真元模型.     

多重线性回归模型的贝叶斯预报分析

多重线性回归模型的贝叶斯预报分析是贝叶斯线性模型理论的重要组成部分。通过模型系统的统计结构，证明了矩阵正态-Wishart分布为模型参数的共轭先验分布；利用贝叶斯定理，根据模型的样本似然函数和参数的先验分布推导了参数的后验分布；然后，从数学上严格推断了模型的预报分布密度函数，证明了模型预报分布为矩阵t分布。研究结果表明：由于参数先验分布的作用，样本的预报分布与其原统计分布有着本质性的差异，前服从矩阵正态分布，而后为矩阵t分布。     

非正态假定下贝叶斯动态线性模型的监控研究

对非正态假定下贝叶斯动态模型，特别是非线性的模型的监控，一直是个难题．本文通过构建基于样本点的统计量，实现了对非正态假定下贝叶斯动态线性模型的监控．该方法也适用于非线性的贝叶斯动态模型．     

纵向数据下半参数联合均值协方差模型的贝叶斯分析

基于改进的Cholesky分解,研究分析了纵向数据下半参数联合均值协方差模型的贝叶斯估计和贝叶斯统计诊断,其中非参数部分采用B样条逼近.主要通过应用Gibbs抽样和Metropolis-Hastings算法相结合的混合算法获得模型中未知参数的贝叶斯估计和贝叶斯数据删除影响诊断统计量.并利用诊断统计量的大小来识别数据的异常点.模拟研究和实例分析都表明提出的贝叶斯估计和诊断方法是可行有效的.     

实证因子模型的贝叶斯半参数分析和模型比较（英文）

为了解决多元数据的异质性,对因子分析模型建立了贝叶斯半参数程序.方法依赖于有限混合分布空间上先验分布的使用.分块吉布斯抽样器用以进行后验分析.L_v测度和贝叶斯因子给出模型比较.基于广义加权中国餐馆算法,给出了半参数模型下数据似然的计算.经验结果显示了方法的有效性.     

Analysis of Multi-Unit Variance Components Models with State Space Profiles

We apply the Kalman Filter to the analysis of multi-unit variance components models where each unit's response profile follows a state space model. We use mixed model results to obtain estimates of unit-specific random effects, state disturbance terms and residual noise terms. We use the signal extraction approach to smooth individual profiles. We show how to utilize the Kalman Filter to efficiently compute the restricted loglikelihood of the model. For the important special case where each unit's response profile follows a continuous structural time series model with known transition matrix we derive an EM algorithm for the restricted maximum likelihood (REML) estimation of the variance components. We present details for the case where individual profiles are modeled as local polynomial trends or polynomial smoothing splines.     

Model-based clustering of probability density functions

Complex data such as those where each statistical unit under study is described not by a single observation (or vector variable), but by a unit-specific sample of several or even many observations, are becoming more and more popular. Reducing these sample data by summary statistics, like the average or the median, implies that most inherent information (about variability, skewness or multi-modality) gets lost. Full information is preserved only if each unit is described by a whole distribution. This new kind of data, a.k.a. “distribution-valued data”, require the development of adequate statistical methods. This paper presents a method to group a set of probability density functions (pdfs) into homogeneous clusters, provided that the pdfs have to be estimated nonparametrically from the unit-specific data. Since elements belonging to the same cluster are naturally thought of as samples from the same probability model, the idea is to tackle the clustering problem by defining and estimating a proper mixture model on the space of pdfs. The issue of model building is challenging here because of the infinite-dimensionality and the non-Euclidean geometry of the domain space. By adopting a wavelet-based representation for the elements in the space, the task is accomplished by using mixture models for hyper-spherical data. The proposed solution is illustrated through a simulation experiment and on two real data sets.     

A Functional Limit Theorem for Observations That Change with Time

Consider a system where units having random magnitude enter according to a Poisson process. While in the system, a unit's magnitude may change with time. In this paper we obtain a functional limit theorem for the sum process of all unit magnitudes present in the system at time t.     

Solving the knapsack problem with imprecise weight coefficients using genetic algorithms

This paper investigates solving the knapsack problem with imprecise weight coefficients using genetic algorithms. This work is based on the assumption that each weight coefficient is imprecise due to decimal truncation or coefficient rough estimation by the decision-maker. To deal with this kind of imprecise data, fuzzy sets provide a powerful tool to model and solve this problem. We investigate the possibility of using genetic algorithms in solving the fuzzy knapsack problem without defining membership functions for each imprecise weight coefficient. The proposed approach simulates a fuzzy number by distributing it into some partition points. We use genetic algorithms to evolve the values in each partition point so that the final values represent the membership grade of a fuzzy number. The empirical results show that the proposed approach can obtain very good solutions within the given bound of each imprecise weight coefficient than the fuzzy knapsack approach. The fuzzy genetic algorithm concept approach is different, but gives better results than the traditional fuzzy approach.     

The Limiting Behavior for Observations That Change with Time

Consider a system where units have random magnitude entering according to a homogeneous or nonhomogeneous Poisson process, while in the system, a unit's magnitude may change with time. In this paper, the authors obtain some results for the limiting behavior of the sum process of all unit magnitudes present in the system at time t.     

Degradation modeling with subpopulation heterogeneities based on the inverse Gaussian process

This study proposes a random effects model based on inverse Gaussian process, where the mixture normal distribution is used to account for both unit-specific and subpopulation-specific heterogeneities. The proposed model can capture heterogeneities due to subpopulations in the same population or the units from different batches. A new Expectation-Maximization (EM) algorithm is developed for point estimation and the bias-corrected bootstrap is used for interval estimation. We show that the EM algorithm updates the parameters based on the gradient of the loglikelihood function via a projection matrix. In addition, the convergence rate depends on the condition number that can be obtained by the projection matrix and the Hessian matrix of the loglikelihood function. A simulation study is conducted to assess the proposed model and the inference methods, and two real degradation datasets are analyzed for illustration.     

Laws of Large Numbers for Observations that Change with Time

Consider a system where units having random magnitude enter according to a nonhomogeneous Poisson process, stay for a random period of time, and then depart. While in the system, a unit's magnitude may change with time. Results are obtained for the strong limiting behavior of the distribution of magnitudes among units present in the system.     

Correlation coefficient of dual hesitant fuzzy sets and its application to multiple attribute decision making

A dual hesitant fuzzy set (DHFS) consists of two parts, that is, the membership hesitancy function and the nonmembership hesitancy function, supporting a more exemplary and flexible access to assign values for each element in the domain, and can handle two kinds of hesitancy in this situation. It can be considered as a powerful tool to express uncertain information in the process of group decision making. Therefore, we propose a correlation coefficient between DHFSs as a new extension of existing correlation coefficients for hesitant fuzzy sets and intuitionistic fuzzy sets and apply it to multiple attribute decision making under dual hesitant fuzzy environments. Through the weighted correlation coefficient between each alternative and the ideal alternative, the ranking order of all alternatives can be determined and the best alternative can be easily identified as well. Finally, a practical example of investment alternatives is given to demonstrate the practicality and effectiveness of the developed approach.     

Computational identification of the lowest space-wise dependent coefficient of a parabolic equation

In the present work, we consider a nonlinear inverse problem of identifying the lowest coefficient of a parabolic equation. The desired coefficient depends on spatial variables only. Additional information about the solution is given at the final time moment, i.e., we consider the final redefinition. An iterative process is used to evaluate the lowest coefficient, where at each iteration we solve the standard initial-boundary value problem for the parabolic equation. On the basis of the maximum principle for the solution of the differential problem, the monotonicity of the iterative process is established along with the fact that the coefficient is approached from above. The possibilities of the proposed computational algorithm are illustrated by numerical examples for a model two-dimensional problem.     

A new aspect of a risk process and its statistical inference

We introduce a new aspect of a risk process, which is a macro approximation of the flow of a risk reserve. We assume that the underlying process consists of a Brownian motion plus negative jumps, and that the process is observed at discrete time points. In our context, each jump size of the process does not necessarily correspond to the each claim size. Therefore our risk process is different from the traditional risk process. We cannot directly observe each jump size because of discrete observations. Our goal is to estimate the adjustment coefficient of our risk process from discrete observations.