A sequential Monte Carlo Gibbs coupled with stochastically approximated expectation-maximization algorithm for functional data

2022 ◽  
Vol 15 (2) ◽  
pp. 197-208
Author(s):  
Ziyue Liu
Keyword(s):  
Monte Carlo ◽  
Expectation Maximization ◽  
Functional Data ◽  
Sequential Monte Carlo ◽  
Expectation Maximization Algorithm

scholarly journals A quantile variant of the expectation–maximization algorithm and its application to parameter estimation with interval data

2018 ◽  
Vol 12 (3) ◽  
pp. 253-272 ◽  
Author(s):  
Chanseok Park
Keyword(s):  
Monte Carlo ◽  
Expectation Maximization ◽  
Likelihood Function ◽  
Expectation Maximization Algorithm ◽  
Parametric Models ◽  
Maximum Likelihood Estimates ◽  
Computational Technique ◽  
Stable Convergence ◽  
Explicit Integration ◽  
Monte Carlo Expectation Maximization

The expectation–maximization algorithm is a powerful computational technique for finding the maximum likelihood estimates for parametric models when the data are not fully observed. The expectation–maximization is best suited for situations where the expectation in each E-step and the maximization in each M-step are straightforward. A difficulty with the implementation of the expectation–maximization algorithm is that each E-step requires the integration of the log-likelihood function in closed form. The explicit integration can be avoided by using what is known as the Monte Carlo expectation–maximization algorithm. The Monte Carlo expectation–maximization uses a random sample to estimate the integral at each E-step. But the problem with the Monte Carlo expectation–maximization is that it often converges to the integral quite slowly and the convergence behavior can also be unstable, which causes computational burden. In this paper, we propose what we refer to as the quantile variant of the expectation–maximization algorithm. We prove that the proposed method has an accuracy of [Formula: see text], while the Monte Carlo expectation–maximization method has an accuracy of [Formula: see text]. Thus, the proposed method possesses faster and more stable convergence properties when compared with the Monte Carlo expectation–maximization algorithm. The improved performance is illustrated through the numerical studies. Several practical examples illustrating its use in interval-censored data problems are also provided.

Reliability Analysis for Masked Data under Type-II Generalized Progressively Hybrid Censored Scheme

2014 ◽  
Vol 687-691 ◽  
pp. 1198-1201
Author(s):  
Bin Liu ◽  
Yi Min Shi ◽  
Jing Cai ◽  
Mo Chen
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Expectation Maximization ◽  
Expectation Maximization Algorithm ◽  
Likelihood Estimation ◽  
Lifetime Data ◽  
Type Ii ◽  
Distribution Parameters ◽  
System Lifetime Data ◽  
Quasi Newton

The Type-II generalized progressively hybrid censored scheme with masked data is presented. Based on masked system lifetime data, using the expectation maximization algorithm and the Quasi-Newton method, we obtain the Maximum Likelihood Estimation (MLE) of the components distribution parameters in the Weibull case. Finally, Monte Carlo simulation is presented to illustrate the effect.

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