基于EM算法隐Markov模型参数估计

描述最大似然参数估计问题,介绍如何用EM算法求解最大似然参数估计.首先给出EM算法的抽象形式,然后介绍EM算法的一个应用:求隐Markov模型中的参数估计.用EM算法推导出隐Markov模型中参数的迭代公式.     

Parameter estimation for partially observable systems subject to random failure

In this paper, we present a parameter estimation procedure for a condition‐based maintenance model under partial observations. Systems can be in a healthy or unhealthy operational state, or in a failure state. System deterioration is driven by a continuous time homogeneous Markov chain and the system state is unobservable, except the failure state. Vector information that is stochastically related to the system state is obtained through condition monitoring at equidistant sampling times. Two types of data histories are available — data histories that end with observable failure, and censored data histories that end when the system has been suspended from operation but has not failed. The state and observation processes are modeled in the hidden Markov framework and the model parameters are estimated using the expectation–maximization algorithm. We show that both the pseudolikelihood function and the parameter updates in each iteration of the expectation–maximization algorithm have explicit formulas. A numerical example is developed using real multivariate spectrometric oil data coming from the failing transmission units of 240‐ton heavy hauler trucks used in the Athabasca oil sands of Alberta, Canada. Copyright © 2012 John Wiley & Sons, Ltd.     

两参数Weibull分布平均寿命的置信下限

王蓉华，徐晓岭．两参数Ｗｅｉｂｕｌ分布平均寿命的置信下限．数理统计与管理，１９９８，１７（２），４３～４５．本文给出了求两参数Ｗｅｉｂｕｌ分布定数截尾下平均寿命置信下限的一种方法     

删失截断情形下失效率变点模型的Bayes参数估计

通过添加部分缺失寿命变量数据,得到了删失截断情形下失效率变点模型相对简单的似然函数.讨论了所添加缺失数据变量的概率分布和随机抽样方法.利用Monte Carlo EM算法对未知参数进行了迭代.结合Metropolis-Hastings算法对参数的满条件分布进行了Gibbs抽样,基于Gibbs样本对参数进行估计,详细介绍了MCMC方法的实施步骤.随机模拟试验的结果表明各参数Bayes估计的精度较高.     

正态分布和瑞利分布混合情形下的参数估计及分类问题

学者往往用单一的分布模拟和拟合杂波,如正态分布、瑞利分布和威布尔分布等。然而在实际中,雷达杂波由多种类型的杂波组成,单一分布通常不能精确刻画雷达杂波规律,因此,应用混合分布模型对雷达杂波数据建模更准确。本文考虑用正态分布和瑞利分布的混合分布拟合杂波,并应用矩估计方法和基于EM算法的极大似然估计方法估计模型参数,最后,应用最大后验概率分类准则验证2种估计方法的分类准确率。通过数据模拟,得出极大似然估计的效果和分类准确率都要优于矩估计的估计效果和分类准确率。     

n维球内均匀分布的参数估计

研究了n维球内均匀分布的参数的点估计与区间估计,利用次序统计量得到了球半径的最大似然估计,在此基础上构造了球半径的无偏估计,并且证明了该无偏估计的相合性.利用构造枢轴量的方法得到了球半径的最短置信区间.     

偏t正态数据下混合线性联合位置与尺度模型的参数估计

偏t正态分布是分析尖峰,厚尾数据的重要统计工具之一.研究提出了偏t正态数据下混合线性联合位置与尺度模型,通过EM算法和Newton-Raphson方法研究了该模型参数的极大似然估计.并通过随机模拟试验验证了所提出方法的有效性.最后,结合实际数据验证了该模型和方法具有实用性和可行性.     

On a proper way to select population failure distribution and a stochastic optimization method in parameter estimation

It is widely accepted that the Weibull distribution plays an important role in reliability applications. The reliability of a product or a system is the probability that the product or the system will still function for a specified time period when operating under some confined conditions. Parameter estimation for the three parameter Weibull distribution has been studied by many researchers in the past. Maximum likelihood has traditionally been the main method of estimation for Weibull parameters along with other recently proposed hybrids of optimization methods. In this paper, we use a stochastic optimization method called the Markov Chain Monte Carlo (MCMC) to carry out the estimation. The method is extremely flexible and inference for any quantity of interest is easily obtained.     

Maximum likelihood estimation in the multi-path change-point problem

Maximum likelihood estimators of the parameters of the distributions before and after the change and the distribution of the time to change in the multi-path change-point problem are derived and shown to be consistent. The maximization of the likelihood can be carried out by using either the EM algorithm or results from mixture distributions. In fact, these two approaches give equivalent algorithms. Simulations to evaluate the performance of the maximum likelihood estimators under practical conditions, and two examples using data on highway fatalities in the United States, and on the health effects of urea formaldehyde foam insulation, are also provided.This work was supported in part by the Natural Science and Engineering Council of Canada, and the Fonds pour la Formation de chercheurs et l'aide à la Recherche Gouvernment du Québec.Lawrence Joseph is also a member of the Department of Epidemiology and Biostatistics of McGill University.     

Weibull分布定时截尾试验数据情形下可靠度的置信限

本文针对Weibull分布定时截尾型试验数据提出了一种计算可靠度置信限的方法。通过采用数据填充的方式将不完全数据虚拟成完全数据,利用完全数据情形下可靠度置信限的计算方法得到删失数据情形下可靠度的置信限。模拟研究表明本文提出的算法具有较好的计算稳定性和可操作性。     

Approximation of the variance gamma model with a finite mixture of normals

We investigate the possibility of approximating the variance gamma distribution with a finite mixture of normals. Therefore, we apply this result to derive a simple historical estimation procedure by means of the Expectation Maximization algorithm.     

Empirical likelihood-based inferences for the area under the ROC curve with covariates

In the receiver operating characteristic (ROC) analysis,the area under the ROC curve (AUC) is a popular summary index of discriminatory accuracy of a diagnostic test.Incorporating covariates into ROC analysis can improve the diagnostic accuracy of the test.Regression model for the AUC is a tool to evaluate the effects of the covariates on the diagnostic accuracy.In this paper,empirical likelihood (EL) method is proposed for the AUC regression model.For the regression parameter vector,it can be shown that the asymptotic distribution of its EL ratio statistic is a weighted sum of independent chi-square distributions.Confidence regions are constructed for the parameter vector based on the newly developed empirical likelihood theorem,as well as for the covariate-specific AUC.Simulation studies were conducted to compare the relative performance of the proposed EL-based methods with the existing method in AUC regression.Finally,the proposed methods are illustrated with a real data set.     

多台设备老炼试验数据情形下的可靠性评估

从统计计算的角度出发,提出多台设备老炼试验可靠性评估方法,并模拟计算了可靠度置信下限的覆盖率、分位点及标准差.结果表明此方法具有可行性和实用性.     

离子通道的混合密度参数估计与状态判别

本文针对多电导水平离子通道的由多个正态分布加权组成的混合分布特点,用EM迭代算法对混合分布中的参数进行极大似然估计,并在此基础上,利用混合分布中最可能的成分判断通道状态,从而还原通道潜在信号,克服了离子通道分析软件PCLAMP中参数估计与状态还原的缺陷。     

二元广义Weibull模型(英文)

本文研究了一个二元广义Weibull分布模型,其边缘分布分别是一元广义Weibull分布.利用EM算法,得到了未知参数的极大似然估计和观测Fisher信息矩阵.     

On nonlinear weighted errors-in-variables parameter estimation problem in the three-parameter Weibull model

This paper is concerned with the three-parameter Weibull distribution which is widely used as a model in reliability and lifetime studies. In practice, the Weibull model parameters are not known in advance and must be estimated from a random sample. Difficulties in applying the method of maximum likelihood to three-parameter Weibull models have led to a variety of alternative approaches in the literature. In this paper we consider the nonlinear weighted errors-in-variables (EIV) fitting approach. As a main result, two theorems on the existence of the EIV estimate are obtained. An illustrative example is also included.     

巴斯卡分布参数p的置信区间

讨论了巴斯卡分布与Beta分布的联系,并通过F分布的分位点给出了参数p的置信水平为1-α的置信区间.     

风速概率分布的参数估计和置信度计算

用Ｗｅｉｂｕｌｌ分布拟合风速了得了很好的效果。本文在三参数Ｗｅｉｂｕｌｌ分布参数估计的基础上，讨论了其置信度问题，有助于对结论可信程度的分析。     

基于左截断右删失数据的单参数Pareto分布参数估计

基于EM算法及极大似然法研究了左截断右删失数据下单参数Pareto分布的参数估计,导出其迭代式,并应用随机模拟对参数估计式进行了模拟检验,结果表明迭代式能够快速收敛,EM估计值较为精确.     

Computational Strategies for Multivariate Linear Mixed-Effects Models With Missing Values

This article presents new computational techniques for multivariate longitudinal or clustered data with missing values. Current methodology for linear mixed-effects models can accommodate imbalance or missing data in a single response variable, but it cannot handle missing values in multiple responses or additional covariates. Applying a multivariate extension of a popular linear mixed-effects model, we create multiple imputations of missing values for subsequent analyses by a straightforward and effective Markov chain Monte Carlo procedure. We also derive and implement a new EM algorithm for parameter estimation which converges more rapidly than traditional EM algorithms because it does not treat the random effects as “missing data,” but integrates them out of the likelihood function analytically. These techniques are illustrated on models for adolescent alcohol use in a large school-based prevention trial.