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Finite mixture of varying coefficient model: Estimation and component selection

JOURNAL OF MULTIVARIATE ANALYSIS 2019年 171卷 452-474页

作者： Ye, Mao Lu, Zhao-Hua Li, Yimei Song, Xinyuan Purdue Univ Dept Stat 610 Purdue Mall W Lafayette IN 47907 USA St Jude Childrens Res Hosp Dept Biostat MS 768262 Danny Thomas Pl Memphis TN 38105 USA Chinese Univ Hong Kong Shenzhen Res Inst Shatin Hong Kong Peoples R China Chinese Univ Hong Kong Dept Stat Shatin Hong Kong Peoples R China

Heterogeneous longitudinal data have become prevalent in medical, biological, and social studies. This paper proposes a finite mixture of varying coefficient models for handling heterogeneous populations. Each component of the mixture is modeled by a varying coefficient mixed-effect model that characterizes the longitudinal relations among variables. The identifiability of the mixture model is studied. Regression splines with equally spaced knots are used to approximate the varying coefficient functions, and a nested expectation maximization algorithm is developed to obtain the maximum likelihood estimation. We propose a penalized likelihood method based on the smoothly clipped absolute deviation (SCAD) penalty for the component selection of finite mixture of varying coefficient model. A modified BIC-based criterion based on the SCAD penalty, the BICSCAD, is proposed for selecting the penalty parameter and spline space simultaneously. The asymptotic properties of parameter estimation and component selection consistency are studied under mild conditions. Simulation studies are conducted to illustrate the component selection, parameter estimation, and inference of the proposed method. The model is then applied to a heterogeneous longitudinal data set from a study of the treatment effect on the use of heroin in the California Civil Addict Program. (C) 2019 Elsevier Inc. All rights reserved.

关键词： expectation maximization algorithm Finite mixture model Model selection Random effects SCAD Varying coefficients

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Detecting DNA regulatory motifs by incorporating positional trends in information content

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GENOME BIOLOGY 2004年第7期5卷 1-21页

作者： Kechris, KJ van Zwet, E Bickel, PJ Eisen, MB Univ Calif Berkeley Dept Stat Berkeley CA 94720 USA Univ Calif Berkeley Lawrence Berkeley Lab Div Life Sci Dept Genome Sci Berkeley CA 94720 USA Univ Calif Berkeley Dept Mol & Cell Biol Ctr Integrat Genom Berkeley CA 94720 USA

On the basis of the observation that conserved positions in transcription factor binding sites are often clustered together, we propose a simple extension to the model-based motif discovery methods. We assign position-specific prior distributions to the frequency parameters of the model, penalizing deviations from a specified conservation profile. Examples with both simulated and real data show that this extension helps discover motifs as the data become noisier or when there is a competing false motif.

关键词： Prior Distribution Change Point Transcription Factor Binding Site Additional Data File expectation maximization algorithm

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4D Flexible Atom-Pairs: An efficient probabilistic conformational space comparison for ligand-based virtual screening

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JOURNAL OF CHEMINFORMATICS 2011年第1期3卷 1-17页

作者： Jahn, Andreas Rosenbaum, Lars Hinselmann, Georg Zell, Andreas Univ Tubingen Ctr Bioinformat Tubingen ZBIT D-72076 Tubingen Germany

Background: The performance of 3D-based virtual screening similarity functions is affected by the applied conformations of compounds. Therefore, the results of 3D approaches are often less robust than 2D approaches. The application of 3D methods on multiple conformer data sets normally reduces this weakness, but entails a significant computational overhead. Therefore, we developed a special conformational space encoding by means of Gaussian mixture models and a similarity function that operates on these models. The application of a model-based encoding allows an efficient comparison of the conformational space of compounds. Results: Comparisons of our 4D flexible atom-pair approach with over 15 state-of-the-art 2D- and 3D-based virtual screening similarity functions on the 40 data sets of the Directory of Useful Decoys show a robust performance of our approach. Even 3D-based approaches that operate on multiple conformers yield inferior results. The 4D flexible atom-pair method achieves an averaged AUC value of 0.78 on the filtered Directory of Useful Decoys data sets. The best 2D- and 3D-based approaches of this study yield an AUC value of 0.74 and 0.72, respectively. As a result, the 4D flexible atom-pair approach achieves an average rank of 1.25 with respect to 15 other state-of-the-art similarity functions and four different evaluation metrics. Conclusions: Our 4D method yields a robust performance on 40 pharmaceutically relevant targets. The conformational space encoding enables an efficient comparison of the conformational space. Therefore, the weakness of the 3D-based approaches on single conformations is circumvented. With over 100,000 similarity calculations on a single desktop CPU, the utilization of the 4D flexible atom-pair in real-world applications is feasible.

关键词： Virtual Screening expectation maximization algorithm Conformational Space Optimal Assignment Conformational Ensemble

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Multiple Content Selections Using Digital Signage Considering Changes in Purchasing Intentions

IEEJ Transactions on Electronics, Information and Systems

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IEEJ Transactions on Electronics, Information and Systems 2024年第12期144卷 1230-1237页

作者： Maeda, Yasunari School of Regional Innovation and Social Design Engineering Kitami Institute of Technology 165 Koen-cho Hokkaido Kitami090-8507 Japan

There is a lot of previous research on sales promotion strategy using digital signage. maximization of expected sales is one of important topics on sales promotion strategy using digital signage. In the previous research, maximization of expected sales considering changes in purchasing intentions for one content selection has been studied. The previous method can not be applied to multiple content selections. In this research, maximization of expected sales considering changes in purchasing intentions for multiple content selections is studied. In the proposed method, the expected sales amount is maximized with respect to a Bayes criterion based on statistical decision theory. The effectiveness of the proposed method is shown by some computational examples. The expected sales amount of the proposed method is greater than that of a comparison target. In this research, the expected sales amount is maximized under the condition that all probabilities are known. But the probabilities are unknown in real cases. An expansion of this research with unknown probabilities is one of further works. © 2024 The Institute of Electrical Engineers of Japan.

关键词： expectation maximization algorithm

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Inference for a series system with dependent masked data under progressive interval censoring

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JOURNAL OF APPLIED STATISTICS 2017年第1期44卷 3-15页

作者： Cai, Jing Shi, Yimin Liu, Bin Northwestern Polytech Univ Dept Appl Math Xian Peoples R China Guizhou Minzu Univ Coll Sci Guiyang Peoples R China

This paper considers the statistical analysis of masked data in a series system with Burr-XII distributed components. Based on progressively Type-I interval censored sample, the maximum likelihood estimators for the parameters are obtained by using the expectation maximization algorithm, and the associated approximate confidence intervals are also derived. In addition, Gibbs sampling procedure using important sampling is applied for obtaining the Bayesian estimates of the parameters, and Monte Carlo method is employed to construct the credible intervals. Finally, a simulation study is proposed to illustrate the efficiency of the methods under different removal schemes and masking probabilities.

关键词： Dependent masked data masking probability progressively Type-I interval censoring expectation maximization algorithm Gibbs sampling Monte Carlo method

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Parameter Estimation for a Bidimensional Partially Observed Ornstein-Uhlenbeck Process with Biological Application

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SCANDINAVIAN JOURNAL OF STATISTICS 2010年第2期37卷 200-220页

作者： Favetto, Benjamin Samson, Adeline Univ Paris 05 Lab MAP5 UMR CNRS 8145 F-75006 Paris France

We consider a bidimensional Ornstein-Uhlenbeck process to describe the tissue microvascularization in anti-cancer therapy. Data are discrete, partial and noisy observations of this stochastic differential equation (SDE). Our aim is to estimate the SDE parameters. We use the main advantage of a one-dimensional observation to obtain an easy way to compute the exact likelihood using the Kalman filter recursion, which allows to implement an easy numerical maximization of the likelihood. Furthermore, we establish the link between the observations and an ARMA process and we deduce the asymptotic properties of the maximum likelihood estimator. We show that this ARMA property can be generalized to a higher dimensional underlying Ornstein-Uhlenbeck diffusion. We compare this estimator with the one obtained by the well-known expectation maximization algorithm on simulated data. Our estimation methods can be directly applied to other biological contexts such as drug pharmacokinetics or hormone secretions.

关键词： ARMA process expectation maximization algorithm hidden Markov model Kalman filter maximum likelihood estimation Ornstein-Uhlenbeck process partial observations

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SENSITIVITY AND SPECIFICITY OF DIAGNOSTIC-TESTS IN ACUTE MAXILLARY SINUSITIS DETERMINED BY MAXIMUM-LIKELIHOOD IN THE ABSENCE OF AN EXTERNAL STANDARD

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JOURNAL OF CLINICAL EPIDEMIOLOGY 1994年第12期47卷 1343-1352页

作者： DEBOCK, GH HOUWINGDUISTERMAAT, JJ SPRINGER, MP KIEVIT, J VANHOUWELINGEN, JC LEIDEN UNIV MED DECIS MAKING UNITLEIDENNETHERLANDS LEIDEN UNIV DEPT MED STAT2300 RA LEIDENNETHERLANDS

This study shows how to obtain maximum likelihood estimates of test sensitivities and specificities in case of lack of an external standard, using the expectation Maximisation (EM) algorithm. This method is used to compare four diagnostic tests in patients suspected of acute maxillary sinusitis. Data were analyzed from published studies. Antral aspiration is the test with the highest diagnostic value. The diagnostic value of a positive clinical examination (according to explicit criteria) and of a positive radiograph or ultrasound are comparable. A negative radiograph is of more diagnostic value than a negative clinical examination or ultrasound. The width of the confidence intervals may be too small, due to model deviations which may give incorrect standard errors. However, the estimated likelihood ratios adequately reflect the relative value of the diagnostic tests considered, even when the assumption of independence is dropped.

关键词： SENSITIVITY AND SPECIFICITY LIKELIHOOD RATIO expectation maximization algorithm ACUTE MAXILLARY SINUSITIS REFERENCE STANDARDS

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Kalman filtering of a space-time Markov random field

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MATHEMATICAL AND COMPUTER MODELLING 2002年第11-13期36卷 1193-1209页

作者： Aggoun, L Sultan Qaboos Univ Dept Math & Stat Al Khoud 123 Oman

In this paper, finite-dimensional recursive filters for space-time Markov random fields are derived. These filters can be used with the expectation maximization (EM) algorithm to yield maximum likelihood estimates of ... 详细信息

关键词： hidden space-time Markov models Kalman filtering expectation maximization algorithm

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Clustering spatial data with a hybrid EM approach

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PATTERN ANALYSIS AND APPLICATIONS 2005年第1-2期8卷 139-148页

作者： Hu, TM Sung, SY HanShan Normal Univ Sch Math & Informat Technol Chaozhou 521041 Guangdong Peoples R China Natl Univ Singapore Dept Comp Sci Singapore 117543 Singapore

In spatial clustering, in addition to the object similarity in the normal attribute space, similarity in the spatial space needs to be considered and objects assigned to the same cluster should usually be close to one another in the spatial space. The conventional expectation maximization (EM) algorithm is not suited for spatial clustering because it does not consider spatial information. Although neighborhood EM (NEM) algorithm incorporates a spatial penalty term to the criterion function., it involves much more iterations in every E-step. In this paper, we propose a Hybrid EM (HEM) approach that combines EM and NEM. Its computational complexity for every pass is between EM and NEM. Experiments also show that its clustering quality is better than EM and comparable to NEM.

关键词： expectation maximization algorithm Gaussian mixture spatial penalty term penalized likelihood spatial clustering spatial autocorrelation

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Efficient and robust estimation for autoregressive regression models using shape mixtures of skewt normal distribution

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METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY 2022年第3期24卷 1519-1551页

作者： Nduka, Uchenna Chinedu Univ Nigeria Dept Stat Nsukka Enugu State Nigeria

Multiple linear regression model based on normally distributed and uncorrelated errors is a popular statistical tool with application in various fields. But these assumptions of normality and no serial correlation are hardly met in real life. Hence, this study considers the linear regression time series model for series with outliers and autocorrelated errors. These autocorrelated errors are represented by a covariance-stationary autoregressive process where the independent innovations are driven by shape mixture of skew-t normal distribution. The shape mixture of skew-t normal distribution is a flexible extension of the skew-t normal with an additional shape parameter that controls skewness and kurtosis. With this error model, stochastic modeling of multiple outliers is possible with an adaptive robust maximum likelihood estimation of all the parameters. An expectation Conditional maximization Either algorithm is developed to carryout the maximum likelihood estimation. We derive asymptotic standard errors of the estimators through an information-based approximation. The performance of the estimation procedure developed is evaluated through Monte Carlo simulations and real life data analysis.

关键词： Autoregressive process expectation maximization algorithm Linear regression model Robust estimation Skew-t-distribution

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