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A generalization of the CIRCE method for quantifying input model uncertainty in presence of several groups of experiments

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NUCLEAR ENGINEERING AND DESIGN 2023年第1期413卷

作者： Damblin, Guillaume Bachoc, Francois Gazzo, Sandro Sargentini, Lucia Ghione, Alberto Univ Paris Saclay CEA DES ISAS DM2SSGLSLIAD F-91191 Gif Sur Yvette France Inst Math Toulouse UMR5219 CNRS F-31062 Toulouse France eXalt 19 Rue Amiens F-59800 Lille France Univ Paris Saclay CEA DES ISAS DM2SSTMFLATF F-91191 Gif Sur Yvette France

The semi-empirical nature of best-estimate models closing the balance equations of thermal-hydraulic (TH) system codes is well-known as a significant source of uncertainty for accuracy of output predictions. This uncertainty, called model uncertainty, is usually represented by multiplicative (log-)Gaussian variables whose estimation requires solving an inverse problem based on a set of adequately chosen real experiments. One method from the TH field, called CIRCE,2 addresses it. We present in the paper a generalization of this method to several groups of experiments each having their own properties, including different ranges for input conditions and different geometries. An individual (log-)Gaussian distribution is therefore estimated for each group in order to investigate whether the model uncertainty is homogeneous between the groups, or should depend on the group. To this end, a multi-group CIRCE is proposed where a variance parameter is estimated for each group jointly to a mean parameter common to all the groups to preserve the uniqueness of the best-estimate model. The ecme algorithm for Maximum Likelihood Estimation developed in Celeux et al. (2010) is extended to the latter context, then applied to relevant demonstration cases. Finally, it is tested on a practical case to assess the uncertainty of critical mass flow assuming two groups due to the difference of geometry between the experimental setups.

关键词： Uncertainty quantification Multi-group CIRCE ecme algorithm Thermal-hydraulic system codes Critical mass flow

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Finite mixture modeling using shape mixtures of the skew scale mixtures of normal distributions

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2020年第12期49卷 3345-3366页

作者： Tamandi, Mostafa Jamalizadeh, Ahad Vali E Asr Univ Rafsanjan Dept Stat Rafsanjan Iran Shahid Bahonar Univ Kerman Fac Math & Comp Dept Stat Kerman Iran

This paper introduces the shape mixtures of the skew scale mixtures of normal distribution which are contained additional shape parameters to regulate skewness and kurtosis. We present a finite mixture model for this new family of distributions, which is a novel model-based tool for clustering heterogeneous data in the presence of skewed and heavy-tailed outcomes. The maximum likelihood estimates of the parameters of the proposed models are obtained by developing an Expectation Conditional Maximization Either algorithm. The numerical performance of the proposed methodology is illustrated through simulated and real data examples.

关键词： Skew-symmetric Finite mixture Shape mixture ecme algorithm

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Symmetrical and asymmetrical mixture autoregressive processes

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BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS 2020年第2期34卷 273-290页

作者： Malekia, Mohsen Hajrajabi, Arezo Arellano-Valle, Reinaldo B. Shiraz Univ Dept Stat Shiraz Iran Imam Khomeini Int Univ Dept Stat Fac Basic Sci Qazvin Iran Univ Catolica Chile Dept Estadist Pontificia Santiago Chile

In this paper, we study the finite mixtures of autoregressive processes assuming that the distribution of innovations (errors) belongs to the class of scale mixture of skew-normal (SMSN) distributions. The SMSN distributions allow a simultaneous modeling of the existence of outliers, heavy tails and asymmetries in the distribution of innovations. Therefore, a statistical methodology based on the SMSN family allows us to use a robust modeling on some non-linear time series with great flexibility, to accommodate skewness, heavy tails and heterogeneity simultaneously. The existence of convenient hierarchical representations of the SMSN distributions facilitates also the implementation of an ecme-type of algorithm to perform the likelihood inference in the considered model. Simulation studies and the application to a real data set are finally presented to illustrate the usefulness of the proposed model.

关键词： ecme algorithm non-linear time series finite mixtures of autoregressive models scale mixtures of skew-normal distributions

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Multivariate-t linear mixed models with censored responses, intermittent missing values and heavy tails

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STATISTICAL METHODS IN MEDICAL RESEARCH 2020年第5期29卷 1288-1304页

作者： Lin, Tsung-, I Wang, Wan-Lun Natl Chung Hsing Univ Inst Stat Taichung Taiwan China Med Univ Dept Publ Hlth Taichung Taiwan Feng Chia Univ Grad Inst Stat & Actuarial Sci Dept Stat Taichung Taiwan

Multivariate longitudinal data arisen in medical studies often exhibit complex features such as censored responses, intermittent missing values, and atypical or outlying observations. The multivariate-t linear mixed model (MtLMM) has been recognized as a powerful tool for robust modeling of multivariate longitudinal data in the presence of potential outliers or fat-tailed noises. This paper presents a generalization of MtLMM, called the MtLMM-CM, to properly adjust for censorship due to detection limits of the assay and missingness embodied within multiple outcome variables recorded at irregular occasions. An expectation conditional maximization either (ecme) algorithm is developed to compute parameter estimates using the maximum likelihood (ML) approach. The asymptotic standard errors of the ML estimators of fixed effects are obtained by inverting the empirical information matrix according to Louis' method. The techniques for the estimation of random effects and imputation of missing responses are also investigated. The proposed methodology is illustrated on two real-world examples from HIV-AIDS studies and a simulation study under a variety of scenarios.

关键词： Censored data ecme algorithm missing values outliers truncated multivariate-t distribution

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Mixtures of restricted skew-t factor analyzers with common factor loadings

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ADVANCES IN DATA ANALYSIS AND CLASSIFICATION 2019年第2期13卷 445-480页

作者： Wang, Wan-Lun Castro, Luis M. Chang, Yen-Ting Lin, Tsung-I Feng Chia Univ Grad Inst Stat & Actuarial Sci Dept Stat Taichung Taiwan Pontificia Univ Catolica Chile Dept Stat Casilla 306Correo 22 Santiago Chile Natl Chung Hsing Univ Inst Stat Taichung Taiwan China Med Univ Dept Publ Hlth Taichung Taiwan

Mixtures of common t factor analyzers (MCtFA) have been shown its effectiveness in robustifying mixtures of common factor analyzers (MCFA) when handling model-based clustering of the high-dimensional data with heavy tails. However, the MCtFA model may still suffer from a lack of robustness against observations whose distributions are highly asymmetric. This paper presents a further robust extension of the MCFA and MCtFA models, called the mixture of common restricted skew-t factor analyzers (MCrstFA), by assuming a restricted multivariate skew-t distribution for the common factors. The MCrstFA model can be used to accommodate severely non-normal (skewed and leptokurtic) random phenomena while preserving its parsimony in factor-analytic representation and performing graphical visualization in low-dimensional plots. A computationally feasible expectation conditional maximization either algorithm is developed to carry out maximum likelihood estimation. The numbers of factors and mixture components are simultaneously determined based on common likelihood penalized criteria. The usefulness of our proposed model is illustrated with simulated and real datasets, and experimental results signify its superiority over some existing competitors.

关键词： Clustering Common factor loadings Data reduction ecme algorithm Factor analyzer Outliers

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Shape mixtures of skew-t-normal distributions: characterizations and estimation

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COMPUTATIONAL STATISTICS 2019年第1期34卷 323-347页

作者： Tamandi, Mostafa Jamalizadeh, Ahad Lin, Tsung-I Shahid Bahonar Univ Kerman Fac Math & Comp Dept Stat Kerman Iran Natl Chung Hsing Univ Inst Stat Taichung 402 Taiwan China Med Univ Dept Publ Hlth Taichung 404 Taiwan

This paper introduces the shape mixtures of the skew-t-normal distribution which is a flexible extension of the skew-t-normal distribution as it contains one additional shape parameter to regulate skewness and kurtosis. We study some of its main characterizations, showing in particular that it is generated through a mixture on the shape parameter of the skew-t-normal distribution when the mixing distribution is normal. We develop an Expectation Conditional Maximization Either algorithm for carrying out maximum likelihood estimation. The asymptotic standard errors of estimators are obtained via the information-based approximation. The numerical performance of the proposed methodology is illustrated through simulated and real data examples.

关键词： Asymmetry ecme algorithm Observed information matrix Robustness Skew-symmetric Truncated normal

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Maximum likelihood estimation in vector autoregressive models with multivariate scaled t-distributed innovations using EM-based algorithms

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2018年第3期47卷 890-904页

作者： Mirniam, A. S. Nematollahi, A. R. Shiraz Univ Dept Stat Shiraz Iran

This article is concerned with the likelihood-based inference of vector autoregressive models with multivariate scaled t-distributed innovations by applying the EM-based (ECM and ecme) algorithms. The ECM and ecme algorithms, which are analytically quite simple to use, are applied to find the maximum likelihood estimates of the model parameters and then compared based on the computational running time and the accuracy of estimation via a simulation study. The results demonstrate that the ecme is efficient and usable in practice. We also show how the method can be applied to a multivariate dataset.

关键词： ECM algorithm ecme algorithm EM algorithm Multivariate scaled t-distribution Vector autoregressive process

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Extending multivariate-t linear mixed models for multiple longitudinal data with censored responses and heavy tails

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STATISTICAL METHODS IN MEDICAL RESEARCH 2018年第1期27卷 48-64页

作者： Wang, Wan-Lun Lin, Tsung-I Lachos, Victor H. Feng Chia Univ Dept Stat Grad Inst Stat & Actuarial Sci Taichung Taiwan Natl Chung Hsing Univ Inst Stat Taichung Taiwan China Med Univ Dept Publ Hlth Taichung Taiwan Univ Estadual Campinas Dept Estat Campinas SP Brazil

The analysis of complex longitudinal data is challenging due to several inherent features: (i) more than one series of responses are repeatedly collected on each subject at irregularly occasions over a period of time;(ii) censorship due to limits of quantification of responses arises left- and/or right- censoring effects;(iii) outliers or heavy-tailed noises are possibly embodied within multiple response variables. This article formulates the multivariate-t linear mixed model with censored responses (MtLMMC), which allows the analysts to model such data in the presence of the above described features simultaneously. An efficient expectation conditional maximization either (ecme) algorithm is developed to carry out maximum likelihood estimation of model parameters. The implementation of the E-step relies on the mean and covariance matrix of truncated multivariate-t distributions. To enhance the computational efficiency, two auxiliary permutation matrices are incorporated into the procedure to determine the observed and censored parts of each subject. The proposed methodology is demonstrated via a simulation study and a real application on HIV/AIDS data.

关键词： AIDS clinical trials censored data ecme algorithm multivariate longitudinal data outliers

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Two-Piece location-scale distributions based on scale mixtures of normal family

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2017年第24期46卷 12356-12369页

作者： Maleki, Mohsen Mahmoudi, Mohammad Reza Shiraz Univ Dept Stat Shiraz Iran Fasa Univ Dept Stat Coll Sci Fasa Iran

In this work, we study the maximum likelihood (ML) estimation problem for the parameters of the two-piece (TP) distribution based on the scale mixtures of normal (SMN) distributions. This is a family of skewed distributions that also includes the scales mixtures of normal class, and is flexible enough for modeling symmetric and asymmetric data. The ML estimates of the proposed model parameters are obtained via an expectation-maximization (EM)-type algorithm.

关键词： ecme algorithm Kurtosis Maximum likelihood estimates Scale mixtures of normal family Skewness Stochastic representation Two-piece distributions

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RANDOM-EFFECTS MIXTURE MODEL WITH AR (1) DEPENDENCE FOR CLASSIFYING LONGITUDINAL CLINICAL DATA

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中国统计学报 2018年第1期56卷 7-24页

作者：林資荃蔡貴鳳

Linear mixed-effects (LME) models have been widely used for longitudinal data analysis as it can account for both fixed and random effects, while simultaneously incorporating the variation on both within and between subjects. The random effects of LME models are commonly assumed to follow a single normal distribution, which may oversimplify the between-subject variability. Mixtures of linear mixed-effects (MLME) models have been proposed to accommodate the heterogeneity problem of random effects. However, the within-subject errors in MLEM models are assumed to be independent for mathematical and computational tractability. In this article, we consider an AR (1) process to address the possible serial autocorrelation among within-subject errors in MLME models. We describe a flexible hierarchical representation of the considered model and develop an efficient Expectation-Conditional Maximization Either (ecme) algorithm for carrying out maximum likelihood estimation. The performance of the proposed method is illustrated on both real and simulated datasets.

关键词： Longitudinal data Random-effects mixture model AR(1) process ecme algorithm

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