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State space functional principal component analysis to identify spatiotemporal patterns in remote sensing lake water quality

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STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT 2021年第12期35卷 2521-2536页

作者： Gong, Mengyi Miller, Claire Scott, Marian O'Donnell, Ruth Simis, Stefan Groom, Steve Tyler, Andrew Hunter, Peter Spyrakos, Evangelos Univ Lancaster Dept Math & Stat Lancaster LA1 4YF England Univ Glasgow Sch Math & Stat Glasgow G12 8QQ Lanark Scotland Plymouth Marine Lab Plymouth PL1 3JH Devon England Univ Stirling Sch Biol & Environm Sci Stirling KF9 4LA Scotland

Satellite remote sensing can provide indicative measures of environmental variables that are crucial to understanding the environment. The spatial and temporal coverage of satellite images allows scientists to investigate the changes in environmental variables in an unprecedented scale. However, identifying spatiotemporal patterns from such images is challenging due to the complexity of the data, which can be large in volume yet sparse within individual images. This paper proposes a new approach, state space functional principal components analysis (SS-FPCA), to identify the spatiotemporal patterns in processed satellite retrievals and simultaneously reduce the dimensionality of the data, through the use of functional principal components. Furthermore our approach can be used to produce interpolations over the sparse areas. An algorithm based on the alternating expectation-conditional maximisation framework is proposed to estimate the model. The uncertainty of the estimated parameters is investigated through a parametric bootstrap procedure. Lake chlorophyll-a data hold key information on water quality status. Such information is usually only available from limited in situ sampling locations or not at all for remote inaccessible lakes. In this paper, the SS-FPCA is used to investigate the spatiotemporal patterns in chlorophyll-a data of Taruo Lake on the Tibetan Plateau, observed by the European Space Agency MEdium Resolution Imaging Spectrometer.

关键词： Functional principal component analysis State space model aecm algorithm Remote sensing images Lake chlorophyll-a

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Robust linear mixed models using the skew t distribution with application to schizophrenia data

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BIOMETRICAL JOURNAL 2010年第4期52卷 449-469页

作者： Ho, Hsiu J. Lin, Tsung-I. Natl Chung Hsing Univ Dept Appl Math Taichung 402 Taiwan Natl Chung Hsing Univ Inst Stat Taichung 402 Taiwan

We consider an extension of linear mixed models by assuming a multivariate skew t distribution for the random effects and a multivariate t distribution for the error terms. The proposed model provides flexibility in capturing the effects of skewness and heavy tails simultaneously among continuous longitudinal data. We present an efficient alternating expectation-conditional maximization (aecm) algorithm for the computation of maximum likelihood estimates of parameters on the basis of two convenient hierarchical formulations. The techniques for the prediction of random effects and intermittent missing values under this model are also investigated. Our methodologies are illustrated through an application to schizophrenia data.

关键词： aecm algorithm Intermittent missing values Outliers Random effects Skew t linear mixed model

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A mixture of generalized hyperbolic factor analyzers

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ADVANCES IN DATA ANALYSIS AND CLASSIFICATION 2016年第4期10卷 423-440页

作者： Tortora, Cristina McNicholas, Paul D. Browne, Ryan P. McMaster Univ Dept Math & Stat Hamilton ON Canada

The mixture of factor analyzers model, which has been used successfully for the model-based clustering of high-dimensional data, is extended to generalized hyperbolic mixtures. The development of a mixture of generalized hyperbolic factor analyzers is outlined, drawing upon the relationship with the generalized inverse Gaussian distribution. An alternating expectation-conditional maximization algorithm is used for parameter estimation, and the Bayesian information criterion is used to select the number of factors as well as the number of components. The performance of our generalized hyperbolic factor analyzers model is illustrated on real and simulated data, where it performs favourably compared to its Gaussian analogue and other approaches.

关键词： Clustering Generalized hyperbolic distribution Mixture of factor analyzers aecm algorithm

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Multivariate t linear mixed models for irregularly observed multiple repeated measures with missing outcomes

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BIOMETRICAL JOURNAL 2013年第4期55卷 554-571页

作者： Wang, Wan-Lun Feng Chia Univ Dept Stat Grad Inst Stat & Actuarial Sci Taichung 40724 Taiwan

Missing outcomes or irregularly timed multivariate longitudinal data frequently occur in clinical trials or biomedical studies. The multivariate t linear mixed model (MtLMM) has been shown to be a robust approach to modeling multioutcome continuous repeated measures in the presence of outliers or heavy-tailed noises. This paper presents a framework for fitting the MtLMM with an arbitrary missing data pattern embodied within multiple outcome variables recorded at irregular occasions. To address the serial correlation among the within-subject errors, a damped exponential correlation structure is considered in the model. Under the missing at random mechanism, an efficient alternating expectation-conditional maximization (aecm) algorithm is used to carry out estimation of parameters and imputation of missing values. The techniques for the estimation of random effects and the prediction of future responses are also investigated. Applications to an HIV-AIDS study and a pregnancy study involving analysis of multivariate longitudinal data with missing outcomes as well as a simulation study have highlighted the superiority of MtLMMs on the provision of more adequate estimation, imputation and prediction performances.

关键词： aecm algorithm Damped exponential model Missing values Outliers Prediction

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DYNAMIC MIXTURES OF FACTOR ANALYZERS TO CHARACTERIZE MULTIVARIATE AIR POLLUTANT EXPOSURES

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ANNALS OF APPLIED STATISTICS 2017年第3期11卷 1617-1648页

作者： Maruotti, Antonello Bulla, Jan Lagona, Francesco Picone, Marco Martella, Francesca Univ Southampton Ctr Innovat & Leadership Hlth Sci Univ Rd Southampton SO17 1BJ Hants England Libera Univ Maria Ss Assunta Dipartimento Sci Econ Polit & Lingue Moderne Via Pompeo Magno 22 I-00192 Rome Italy Univ Bergen Dept Math Allegaten 41 N-5007 Bergen Norway Univ Rome Tre Dipartimento Sci Polit Via Grabriello Chiabrera 199 I-00145 Rome Italy Inst Environm Protect & Res ISPRA Dipartimento Tutela Acque Interne & Marine Via Brancati 48 I-00144 Rome Italy Sapienza Univ Roma Dipartimento Sci Stat Piazzale Aldo Moro 5 I-00185 Rome Italy

The assessment of pollution exposure is based on the analysis of a multivariate time series that include the concentrations of several pollutants as well as the measurements of multiple atmospheric variables. It typically requires methods of dimensionality reduction that are capable of identifying potentially dangerous combinations of pollutants and simultaneously segmenting exposure periods according to air quality conditions. When the data are high-dimensional, however, efficient methods of dimensionality reduction are challenging because of the formidable structure of cross-correlations that arise from the dynamic interaction between weather conditions and natural/anthropogenic pollution sources. In order to assess pollution exposure in an urban area while taking the above mentioned difficulties into account, we have developed a class of parsimonious hidden Markov models. In a multivariate time series setting, this approach simultaneously allows for the performance of temporal segmentation and dimensionality reduction. We specifically approximate the distribution of multiple pollutant concentrations by mixtures of factor analysis models, whose parameters evolve according to a latent Markov chain. Covariates are included as predictors of the chain transition probabilities. Parameter constraints on the factorial component of the model are exploited to tune the flexibility of dimensionality reduction. In order to estimate the model parameters efficiently, we have proposed a novel three-step Alternating Expected Conditional Maximization (aecm) algorithm, which is also assessed in a simulation study. In the case study, the proposed methods could (1) describe the exposure to pollution in terms of a few latent regimes, (2) associate these regimes with specific combinations of pollutant concentration levels as well as distinct correlation structures between concentrations, and (3) capture the influence of weather conditions on transitions between regimes.

关键词： Hidden Markov models aecm algorithm dimensionality reduction three-step algorithm

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An efficient ECM algorithm for maximum likelihood estimation in mixtures of t-factor analyzers

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COMPUTATIONAL STATISTICS 2013年第2期28卷 751-769页

作者： Wang, Wan-Lun Lin, Tsung-I Feng Chia Univ Dept Stat Taichung 40724 Taiwan Natl Chung Hsing Univ Inst Stat Taichung 402 Taiwan China Med Univ Dept Publ Hlth Taichung Taiwan

Mixture of t factor analyzers (MtFA) have been shown to be a sound model-based tool for robust clustering of high-dimensional data. This approach, which is deemed to be one of natural parametric extensions with respect to normal-theory models, allows for accommodation of potential noise components, atypical observations or data with longer-than-normal tails. In this paper, we propose an efficient expectation conditional maximization (ECM) algorithm for fast maximum likelihood estimation of MtFA. The proposed algorithm inherits all appealing properties of the ordinary EM algorithm such as its stability and monotonicity, but has a faster convergence rate since its CM steps are governed by a much smaller fraction of missing information. Numerical experiments based on simulated and real data show that the new procedure outperforms the commonly used EM and aecm algorithms substantially in most of the situations, regardless of how the convergence speed is assessed by the computing time or number of iterations.

关键词： aecm algorithm ECM algorithm EM algorithm Maximum likelihood estimation MFA MtFA

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Model-based clustering of censored data via mixtures of factor analyzers

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2019年 140卷 104-121页

作者： Wang, Wan-Lun Castro, Luis M. Lachos, Victor H. Lin, Tsung-I Feng Chia Univ Grad Inst Stat & Actuarial Sci Dept Stat Taichung 40724 Taiwan Pontificia Univ Catolica Chile Dept Stat Casilla 306Correo 22 Santiago Chile Millennium Nucleus Ctr Discovery Struct Complex D Santiago Chile Pontificia Univ Catolica Chile Ctr Riesgos & Seguros UC Santiago Chile Univ Connecticut Dept Stat Storrs CT 06269 USA Natl Chung Hsing Univ Inst Stat Taichung 402 Taiwan China Med Univ Dept Publ Hlth Taichung 404 Taiwan

Mixtures of factor analyzers (MFA) provide a promising tool for modeling and clustering high-dimensional data that contain an overwhelmingly large number of attributes measured on individuals arisen from a heterogeneous population. Due to the restriction of experimental apparatus, measurements can be limited to some lower and/or upper detection bounds and thus the data are possibly censored. In this paper, we extend the MFA to accommodate censored data, and the new model is called the MFA with censoring (MFAC). A computationally feasible alternating expectation conditional maximization (aecm) algorithm is developed to carry out maximum likelihood estimation of the MFAC model. Practical issues related to model-based clustering and recovery of censored data are also discussed. Simulation studies are conducted to examine the effect of censoring in classification, estimation and cluster validation. We also present an application of the proposed approach to two real data examples in which a certain number of left-censored observations are present. (C) 2019 Elsevier B.V. All rights reserved.

关键词： aecm algorithm Censored data Detection limit Outright clustering Truncated multivariate normal distribution

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Model-based clustering of multivariate ordinal data relying on a stochastic binary search algorithm

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STATISTICS AND COMPUTING 2016年第5期26卷 929-943页

作者： Biernacki, Christophe Jacques, Julien Univ Lille 1 Lab Painleve F-59655 Villeneuve Dascq France Univ Lille 1 Inria F-59655 Villeneuve Dascq France Univ Lyon 2 Lab ERIC F-69676 Bron France

We design a probability distribution for ordinal data by modeling the process generating data, which is assumed to rely only on order comparisons between categories. Contrariwise, most competitors often either forget the order information or add a non-existent distance information. The data generating process is assumed, from optimality arguments, to be a stochastic binary search algorithm in a sorted table. The resulting distribution is natively governed by two meaningful parameters (position and precision) and has very appealing properties: decrease around the mode, shape tuning from uniformity to a Dirac, identifiability. Moreover, it is easily estimated by an EM algorithm since the path in the stochastic binary search algorithm can be considered as missing values. Using then the classical latent class assumption, the previous univariate ordinal model is straightforwardly extended to model-based clustering for multivariate ordinal data. Parameters of this mixture model are estimated by an aecm algorithm. Both simulated and real data sets illustrate the great potential of this model by its ability to parsimoniously identify particularly relevant clusters which were unsuspected by some traditional competitors.

关键词： Ordinal data Binary search algorithm Latent variables aecm algorithm

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Convergence properties of the EM algorithm in constrained parameter spaces

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CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE 1999年第3期27卷 639-648页

作者： Nettleton, D Univ Nebraska Dept Math & Stat Lincoln NE 68588 USA

The established general results on convergence properties of the EM algorithm require the sequence of EM parameter estimates to fall in the interior of the parameter space over which the likelihood is being maximized. This paper presents convergence properties of the EM sequence of likelihood values and parameter estimates in constrained parameter spaces for which the sequence of EM parameter estimates may converge to the boundary of the constrained parameter space contained in the interior of the unconstrained parameter space. Examples of the behavior of the EM algorithm applied to such parameter spaces are presented.

关键词： EM algorithm GEM algorithm ECM algorithm aecm algorithm incomplete data inequality constraints order-restricted inference restricted maximum-likelihood estimate

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Mixtures of factor analyzers with covariates for modeling multiply censored dependent variables

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STATISTICAL PAPERS 2021年第5期62卷 2119-2145页

作者： Wang, Wan-Lun Castro, Luis M. Hsieh, Wan-Chen Lin, Tsung-, I Feng Chia Univ Dept Stat Grad Inst Stat & Actuarial Sci Taichung 40724 Taiwan Pontificia Univ Catolica Chile Dept Stat Casilla 306Correo 22 Santiago Chile Millennium Nucleus Ctr Discovery Struct Complex D Santiago Chile Pontificia Univ Catolica Chile Ctr Riesgos & Seguros UC Santiago Chile Natl Chung Hsing Univ Inst Stat Taichung 402 Taiwan China Med Univ Dept Publ Hlth Taichung 404 Taiwan

Censored data arise frequently in diverse applications in which observations to be measured may be subject to some upper and lower detection limits due to the restriction of experimental apparatus such that they are not exactly quantifiable. Mixtures of factor analyzers with censored data (MFAC) have been recently proposed for model-based density estimation and clustering of high-dimensional data in the presence of censored observations. In this paper, we consider an extended version of MFAC by considering regression equations to describe the relationship between covariates and multiply censored dependent variables. Two analytically feasible EM-type algorithms are developed for computing maximum likelihood estimates of model parameters with closed-form expressions. Moreover, we provide an information-based method to compute asymptotic standard errors of mixing proportions and regression coefficients. The utility and performance of our proposed methodology are illustrated through a simulation study and two real data examples.

关键词： aecm algorithm Censored data Detection limit Factor analysis ML estimation Truncated multivariate normal distribution

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