scholarly journals Uniqueness of Maximum Likelihood Estimators for a Backup System in a Condition-Based Maintenance

2012 ◽  
Vol 2012 ◽  
pp. 1-5
Author(s):  
Qihong Duan ◽  
Ying Wei ◽  
Xiang Chen
Keyword(s):  
Maximum Likelihood ◽  
Em Algorithm ◽  
Maximum Likelihood Estimators ◽  
Condition Based Maintenance ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Process Data ◽  
Parameter Estimation Problem ◽  
Backup System ◽  
The Em Algorithm

A parameter estimation problem for a backup system in a condition-based maintenance is considered. We model a backup system by a hidden, three-state continuous time Markov process. Data are obtained through condition monitoring at discrete time points. Maximum likelihood estimates of the model parameters are obtained using the EM algorithm. We establish conditions under which there is no more than one limitation in the parameter space for any sequence derived by the EM algorithm.

scholarly journals Fast Computation of the EM Algorithm for Mixture Models

2021 ◽  
Author(s):  
Masahiro Kuroda
Keyword(s):  
Maximum Likelihood ◽  
Em Algorithm ◽  
Mixture Models ◽  
Computation Time ◽  
Likelihood Estimation ◽  
Heterogeneous Data ◽  
Maximum Likelihood Estimates ◽  
The Em Algorithm ◽  
Clustering And Classification ◽  
Number Of Iterations

Mixture models become increasingly popular due to their modeling flexibility and are applied to the clustering and classification of heterogeneous data. The EM algorithm is largely used for the maximum likelihood estimation of mixture models because the algorithm is stable in convergence and simple in implementation. Despite such advantages, it is pointed out that the EM algorithm is local and has slow convergence as the main drawback. To avoid the local convergence of the EM algorithm, multiple runs from several different initial values are usually used. Then the algorithm may take a large number of iterations and long computation time to find the maximum likelihood estimates. The speedup of computation of the EM algorithm is available for these problems. We give the algorithms to accelerate the convergence of the EM algorithm and apply them to mixture model estimation. Numerical experiments examine the performance of the acceleration algorithms in terms of the number of iterations and computation time.

scholarly journals Parameter Estimation of a Multistate Model for an Aging Piece of Equipment under Condition-Based Maintenance

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Qihong Duan ◽  
Xiang Chen ◽  
Dengfu Zhao ◽  
Zheng Zhao
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Model Calculation ◽  
Expectation Maximization ◽  
Expectation Maximization Algorithm ◽  
Condition Based Maintenance ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Simulation Studies ◽  
Multistate Model

We study a multistate model for an aging piece of equipment under condition-based maintenance and apply an expectation maximization algorithm to obtain maximum likelihood estimates of the model parameters. Because of the monitoring discontinuity, we cannot observe any state's duration. The observation consists of the equipment's state at an inspection or right after a repair. Based on a proper construction of stochastic processes involved in the model, calculation of some probabilities and expectations becomes tractable. Using these probabilities and expectations, we can apply an expectation maximization algorithm to estimate the parameters in the model. We carry out simulation studies to test the accuracy and the efficiency of the algorithm.

scholarly journals Two-part quantile regression models for semi-continuous longitudinal data: A finite mixture approach

2021 ◽  
pp. 1471082X2199360
Author(s):  
Luca Merlo ◽  
Antonello Maruotti ◽  
Lea Petrella
Keyword(s):  
Longitudinal Data ◽  
Em Algorithm ◽  
Quantile Regression ◽  
Finite Mixture ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Quantile Regression Model ◽  
The Em Algorithm ◽  
Binary Response Variable ◽  
Rand Health Insurance Experiment

This article develops a two-part finite mixture quantile regression model for semi-continuous longitudinal data. The proposed methodology allows heterogeneity sources that influence the model for the binary response variable to also influence the distribution of the positive outcomes. As is common in the quantile regression literature, estimation and inference on the model parameters are based on the asymmetric Laplace distribution. Maximum likelihood estimates are obtained through the EM algorithm without parametric assumptions on the random effects distribution. In addition, a penalized version of the EM algorithm is presented to tackle the problem of variable selection. The proposed statistical method is applied to the well-known RAND Health Insurance Experiment dataset which gives further insights on its empirical behaviour.

Unsupervised Learning Through Generalized Mixture Model

2021 ◽  
Author(s):  
Samyajoy Pal ◽  
Christian Heumann
Keyword(s):  
Cluster Analysis ◽  
Maximum Likelihood ◽  
Em Algorithm ◽  
Unsupervised Learning ◽  
Mixture Models ◽  
Mixture Model ◽  
Learning Problems ◽  
Point Estimate ◽  
Model Parameters ◽  
The Em Algorithm

Abstract A generalized way of building mixture models using different distributions is explored in this article. The EM algorithm is used with some modifications to accommodate different distributions within the same model. The model uses any point estimate available for the respective distributions to estimate the mixture components and model parameters. The study is focused on the application of mixture models in unsupervised learning problems, especially cluster analysis. The convenience of building mixture models using the generalized approach is further emphasised by appropriate examples, exploiting the well-known maximum likelihood and Bayesian estimates of the parameters of the parent distributions.

scholarly journals Maximum Likelihood Estimation using the EM Algorithm

2021 ◽  
Vol 8 (9) ◽  
pp. 275-277
Author(s):  
Ahsene Lanani
Keyword(s):  
Missing Data ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Em Algorithm ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Likelihood Estimation ◽  
Mixed Linear Model ◽  
Model Parameters ◽  
The Em Algorithm

This paper yields with the Maximum likelihood estimation using the EM algorithm. This algorithm is very used to solve nonlinear equations with missing data. We estimated the linear mixed model parameters and those of the variance-covariance matrix. The considered structure of this matrix is not necessarily linear. Keywords: Algorithm EM; Maximum likelihood; Mixed linear model.

EM Algorithm Based on Fuzzification and its Application

2012 ◽  
Vol 532-533 ◽  
pp. 1445-1449
Author(s):  
Ting Ting Tong ◽  
Zhen Hua Wu
Keyword(s):  
Em Algorithm ◽  
Mixed Model ◽  
Image Data ◽  
Training Sample ◽  
Model Parameters ◽  
Parameter Learning ◽  
Weighted Degree ◽  
The Em Algorithm ◽  
The Impact

EM algorithm is a common method to solve mixed model parameters in statistical classification of remote sensing image. The EM algorithm based on fuzzification is presented in this paper to use a fuzzy set to represent each training sample. Via the weighted degree of membership, different samples will be of different effect during iteration to decrease the impact of noise on parameter learning and to increase the convergence rate of algorithm. The function and accuracy of classification of image data can be completed preferably.

Maximum-likelihood estimation in linkage heterogeneity models including additional information via the EM algorithm

1995 ◽  
Vol 12 (5) ◽  
pp. 515-527 ◽  
Author(s):  
Jeanine J. Houwing-Duistermaat ◽  
Lodewijk A. Sandkuijl ◽  
Arthur A. B. Bergen ◽  
Hans C. van Houwelingen
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Em Algorithm ◽  
Likelihood Estimation ◽  
Additional Information ◽  
The Em Algorithm

scholarly journals A Family of Loss Distributions with an Application to the Vehicle Insurance Loss Data

2019 ◽  
pp. 731-744 ◽  
Author(s):  
Zubair Ahmad Ahmad ◽  
Eisa Mahmoudi Mahmoudi ◽  
G. G. Hamedani
Keyword(s):  
Maximum Likelihood ◽  
Financial Risk ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Set ◽  
Loss Model ◽  
New Class ◽  
Proposed Model ◽  
Loss Distributions ◽  
Loss Data

Actuaries are often in search of nding an adequate loss model in the scenario of actuarial and financial risk management problems. In this work, we propose a new approach to obtain a new class of loss distributions. A special sub-model of the proposed family, called the Weibull-loss model isconsidered in detail. Some mathematical properties are derived and maximum likelihood estimates of the model parameters are obtained. Certain characterizations of the proposed family are also provided. A simulation study is done to evaluate the performance of the maximum likelihood estimators. Finally, an application of the proposed model to the vehicle insurance loss data set is presented.

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