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Modelling and analysing the daily temperature of several cities using mixture Gaussian distributions

INTERNATIONAL JOURNAL OF COMPUTING SCIENCE AND MATHemATICS 2023年第4期17卷 320-341页

作者： Al-Hemyari, Zuhair A. Al Abbasi, Jamal N. Univ Nizwa CAS Dept Math & Phys Sci POB 33 Nizwa 616 Oman AL Nahrain Univ Dept Stat Baghdad Iraq

The rise in the surface temperature of the Earth since the 19th century is a clear indication of the negative and significant impact humans have had upon it. One of the results of this is that many researchers have studied meteorological problems. Some of the important applications for modelling the daily maximum and minimum temperatures reveal the importance of modelling the data for these phenomena using mixed distributions. In order to model the data of three cities over 40 years of daily maximum/minimum temperatures, heavy statistical computations have been carried out, and several single and mixture Gaussian distributions have developed the modelling of data of three cities for the period of 1980-2019 of daily maximum/minimum temperatures. In addition, the computations of expectation maximisation algorithm estimators, the tests of goodness, and the frequency distributions have been developed to carry out accurate analyses. The data is analysed, several indicators are seized, and the conclusions, recommendations, limitations, and future research directions are discussed.

关键词： Gaussian distribution mixture distributions MLE em algorithms goodness of fit Kolmogorov-Smirnov test Anderson-Darling test daily temperatures

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Robust estimation using multivariate t innovations for vector autoregressive models via ECM algorithm

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JOURNAL OF APPLIED STATISTICS 2021年第4期48卷 693-711页

作者： Nduka, Uchenna C. Ugah, Tobias E. Izunobi, Chinyeaka H. Univ Nigeria Dept Stat Nsukka Nigeria Fed Univ Technol Owerri Dept Stat Owerri Nigeria

This paper considers the vector autoregressive model of order p, VAR(p), with multivariate t error distributions, the latter being more prevalent in real life than the usual multivariate normal distribution. It is believed that the maximum-likelihood equations for the multivariate t distribution have convergence problem, hence we develop estimation procedures for VAR(p) model using the normal mean-variance mixture representation of multivariate t distribution. The procedure relies on the computational ease available in Expectation Maximization-based algorithms. The estimators obtained are explicit functions of sample observations and therefore are easy to compute. Extensive simulation experiments show that the estimators have negligible bias and are considerably more efficient than an existing method that uses the least-squares error approach. It is shown that the proposed estimators are robust to plausible deviations from an assumed distribution and hence are more advantageous when compared with the other estimator. One real-life example is given for illustration purposes.

关键词： em algorithms maximum likelihood estimation multivariate t distribution robust estimation vector autoregressive model

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State Estimation Schemes for Independent Component Coupled Hidden Markov Models

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STOCHASTIC ANALYSIS AND APPLICATIONS 2010年第3期28卷 430-446页

作者： Malcolm, W. P. Quadrianto, Novi Aggoun, Lakhdar Australian Natl Univ Inst Math Sci Canberra ACT 0200 Australia Natl Informat Commun Technol Ctr Australia NICTA Canberra ACT Australia Sultan Qaboos Univ Dept Math & Stat Muscat Oman

Conventional Hidden Markov models generally consist of a Markov chain observed through a linear map corrupted by additive noise. This general class of model has enjoyed a huge and diverse range of applications, for example, speech processing, biomedical signal processing and more recently quantitative finance. However, a lesser known extension of this general class of model is the so-called Factorial Hidden Markov Model (FHMM). FHMMs also have diverse applications, notably in machine learning, artificial intelligence and speech recognition [13, 17]. FHMMs extend the usual class of HMMs, by supposing the partially observed state process is a finite collection of distinct Markov chains, either statistically independent or dependent. There is also considerable current activity in applying collections of partially observed Markov chains to complex action recognition problems, see, for example, [6]. In this article we consider the Maximum Likelihood (ML) parameter estimation problem for FHMMs. Much of the extant literature concerning this problem presents parameter estimation schemes based on full data log-likelihood em algorithms. This approach can be slow to converge and often imposes heavy demands on computer memory. The latter point is particularly relevant for the class of FHMMs where state space dimensions are relatively large. The contribution in this article is to develop new recursive formulae for a filter-based em algorithm that can be implemented online. Our new formulae are equivalent ML estimators, however, these formulae are purely recursive and so, significantly reduce numerical complexity and memory requirements. A computer simulation is included to demonstrate the performance of our results.

关键词： Change of measure techniques em algorithms Factorial hidden Markov models Filtering Martingales M-ary detection Parameter estimation Smoothing

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Simulation-Based Performance Evaluation of Missing Data Handling in Network Analysis

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MULTIVARIATE BEHAVIORAL RESEARCH 2024年第3期59卷 461-481页

作者： Nehler, Kai Jannik Schultze, Martin Goethe Univ Frankfurt Dept Psychol Frankfurt Germany Goethe Univ Frankfurt Dept Psychol Theodor W Adorno Pl 6 D-60323 Frankfurt Germany

Network analysis has gained popularity as an approach to investigate psychological constructs. However, there are currently no guidelines for applied researchers when encountering missing values. In this simulation study, we compared the performance of a two-step em algorithm with separated steps for missing handling and regularization, a combined direct em algorithm, and pairwise deletion. We investigated conditions with varying network sizes, numbers of observations, missing data mechanisms, and percentages of missing values. These approaches are evaluated with regard to recovering population networks in terms of loss in the precision matrix, edge set identification and network statistics. The simulation showed adequate performance only in conditions with large samples (n >= 500) or small networks (p = 10). Comparing the missing data approaches, the direct em appears to be more sensitive and superior in nearly all chosen conditions. The two-step em yields better results when the ratio of n/p is very large - being less sensitive but more specific. Pairwise deletion failed to converge across numerous conditions and yielded inferior results overall. Overall, direct em is recommended in most cases, as it is able to mitigate the impact of missing data quite well, while modifications to two-step em could improve its performance.

关键词： Network analysis missing values simulation study graphical lasso regularization em algorithms

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Multiple Fault Detection Using Multi-rate Probability Principal Component Analysis Models

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IFAC-PapersOnLine 2017年第1期50卷 14752-14757页

作者： Zhou, Le Chen, Junghui Ge, Zhiqiang Song, Zhihuan School of Automation and Electrical Engineering Zhejiang University of Science & Technology ZhejiangHangzhou310023 China Department of Chemical Engineering Chung-Yuan Christian University Chung-Li320 Taiwan State Key Laboratory of Industrial Control Technology Zhejiang University Hangzhou310027 China

In most chemical processes, both online measurements and offline laboratory analysis can be obtained at different sampling rates. Usually, the online process variables are frequently sampled while the key quality indicators are analyzed at irregular time, sometimes on hourly and sometimes daily basis. To effectively integrate different classes of measurements in a multi-rate process, a multi-rate probability principal component analysis (MPPCA) model is proposed to utilize the efficiently collected data and to improve the performance on both model prediction and process monitoring. In MPPCA, the model parameters are calibrated by the expectation-maximization algorithm. The proposed method is able to handle irregular samples in measurements and incorporate all the observations for model training. Also, the corresponding statistics based on MPPCA is developed for the fault detection purpose. Finally, a TE benchmark is presented to illustrate the effectiveness of the proposed methods. © 2017

关键词： Principal component analysis Chemical analysis Fault detection Image segmentation Maximum principle Probability Process monitoring Quantum theory Chemical process em algorithms Expectation maximization algorithms Key quality indicators Laboratory analysis Multi rate On line measurement Probability principal component analysis

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New estimation and feature selection methods in mixture-of-experts models

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CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE 2010年第4期38卷 519-539页

作者： Khalili, Abbas McGill Univ Dept Math & Stat Montreal PQ H3A 2K6 Canada

We study estimation and feature selection problems in mixture of-experts models An l(2) penalized maximum likelihood estimator is proposed as an alternative to the ordinary maximum likelihood estimator The estimator is particularly advantageous when fitting a mixture-of experts model to data with many correlated features It is shown that the proposed estimator is root n consistent and simulations show its superior finite sample behaviour compared to that of the maximum likelihood estimator For feature selection two extra penalty functions are applied to the l(2)-penalized log likelihood function The proposed feature selection method is computationally much more efficient than the popular all-subset selection methods Theoretically it is shown that the method is consistent in feature selection and simulations support our theoretical results A real-data example is presented to demonstrate the method The Canadian Journal of Statistics 38 519-539 2010 (C) 2010 Statistical Society of Canada

关键词： Mixture-of experts regularization LASSO SCAD em algorithms

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Spatial sampling design based on stochastic complexity

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JOURNAL OF MULTIVARIATE ANALYSIS 1999年第1期71卷 94-110页

作者： Bueso, MC Angulo, JM Qian, G Alonso, FJ Univ Granada Dept Estadist & Invest Operat E-18071 Granada Spain La Trobe Univ Sch Stat Sci Bundoora Vic 3083 Australia

A new methodology is introduced for spatial sampling design when the variable of interest cannot be directly observed, but information on it can be obtained by sampling a related variable, and estimation of the underlying model is required. An approach based on entropy has been proposed by Bueso. Angulo, and Alonso (1198, Environ. Ecol. Statist. 5. No. 1, 29-44) in the case where a model for the involved variables is given. However. in some cases a predetermined structure modelling the behaviour of the variables cannot be assumed. In this context, we derive criteria ibr solving the design problem based on the stochastic complexity theory and on the philosophy of the em algorithm. For applying the proposed criteria a computational procedure is developed based on the supplemented em algorithms. The methodology is illustrated with a numerical example. (C) 1999 Academic Press.

关键词： em algorithms incomplete data minimum description length network design stochastic complexity

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MODEL-BASED CLUSTERING OF LARGE NETWORKS

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ANNALS OF APPLIED STATISTICS 2013年第2期7卷 1010-1039页

作者： Vu, Duy Q. Hunter, David R. Schweinberger, Michael Univ Melbourne Dept Math & Stat Melbourne Vic 3010 Australia Penn State Univ Dept Stat University Pk PA 16802 USA Rice Univ Dept Stat Houston TX 77251 USA

We describe a network clustering framework, based on finite mixture models, that can be applied to discrete-valued networks with hundreds of thousands of nodes and billions of edge variables. Relative to other recent model-based clustering work for networks, we introduce a more flexible modeling framework, improve the variational-approximation estimation algorithm, discuss and implement standard error estimation via a parametric bootstrap approach, and apply these methods to much larger data sets than those seen elsewhere in the literature. The more flexible framework is achieved through introducing novel parameterizations of the model, giving varying degrees of parsimony, using exponential family models whose structure may be exploited in various theoretical and algorithmic ways. The algorithms are based on variational generalized em algorithms, where the E-steps are augmented by a minorization-maximization (MM) idea. The bootstrapped standard error estimates are based on an efficient Monte Carlo network simulation idea. Last, we demonstrate the usefulness of the model-based clustering framework by applying it to a discrete-valued network with more than 131,000 nodes and 17 billion edge variables.

关键词： Social networks stochastic block models finite mixture models em algorithms generalized em algorithms variational em algorithms MM algorithms

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Modeling the length-of-stay of patients with geriatric diseases or alcohol use disorder using phase-type distributions with covariates

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IISE TRANSACTIONS ON HEALTHCARE SYSTemS ENGINEERING 2021年第3期11卷 181-191页

作者： Gu, Wanlu Fan, Neng Liao, Haitao Univ Arizona Dept Syst & Ind Engn Tucson AZ 85721 USA Univ Arkansas Dept Ind Engn Fayetteville AR USA

The hospital length-of-stay (LOS), as an important measure of the effectiveness of healthcare, represents the level of medical requirement and is highly related to the treatment costs. As the human life expectancy has being increased rapidly in the past few decades, there is a pressing need to improve health systems for geriatric patients. Similarly, the alcohol use disorder (AUD), as a chronic relapsing brain disease related to severe problem drinking, has caused negative impacts to society and put patients' health and safety at risk. In both cases, more efficient hospital management is in demand due to increasing requirements for long-term hospital treatment and the continuously rising medical cost. In order to improve the healthcare efficiency, an accurate modeling of the LOS data and the further analysis of potential influencing factors are necessary. In this paper, we utilize the Coxian Phase-Type (PH) distribution and apply Maximum Likelihood Estimation (MLE) to fit the patient flow information of both geriatric patients and AUD patients collected in a hospital. The influences of the covariates of age, gender, admission type, admit source, and financial class on LOS are assessed and compared through Expectation-Maximization (em) algorithms. The results show that the LOS data of both types of patients can be modeled well, and the differences with respect to covariates can be accurately identified by the proposed methods. Using the fitted Coxian PH distribution and the estimated coefficients of covariates will provide a guide for better decision-making in healthcare service and resource allocation.

关键词： Phase-type distribution healthcare quality length-of-stay covariate em algorithms

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Post-processing Multiensemble Temperature and Precipitation Forecasts Through an Exchangeable Normal-Gamma Model and Its Tobit Extension

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JOURNAL OF AGRICULTURAL BIOLOGICAL AND ENVIRONMENTAL STATISTICS 2019年第2期24卷 309-345页

作者： Courbariaux, Marie Barbillon, Pierre Perreault, Luc Parent, Eric Univ Paris Saclay INRA AgroParisTech UMR MIA Paris F-75005 Paris France Hydro Quebec Res Inst Varennes PQ Canada

Meteorological ensemble members are a collection of scenarios for future weather issued by a meteorological center. Such ensembles nowadays form the main source of valuable information for probabilistic forecasting which aims at producing a predictive probability distribution of the quantity of interest instead of a single best guess point-wise estimate. Unfortunately, ensemble members cannot generally be considered as a sample from such a predictive probability distribution without a preliminary post-processing treatment to re-calibrate the ensemble. Two main families of post-processing methods, either competing such as the BMA or collaborative such as the emOS, can be found in the literature. This paper proposes a mixed-effect model belonging to the collaborative family. The structure of the model is formally justified by Bruno de Finetti's representation theorem which shows how to construct operational statistical models of ensemble based on judgments of invariance under the relabeling of the members. Its interesting specificities are as follows: (1) exchangeability contributes to parsimony, with an interpretation of the latent pivot of the ensemble in terms of a statistical synthesis of the essential meteorological features of the ensemble members, (2) a multiensemble implementation is straightforward, allowing to take advantage of various information so as to increase the sharpness of the forecasting procedure. Focus is cast onto normal statistical structures, first with a direct application for temperatures, then with its very convenient Tobit extension for precipitation. Inference is performed by expectation maximization (em) algorithms with both steps leading to explicit analytic expressions in the Gaussian temperature case, and recourse is made to stochastic conditional simulations in the zero-inflated precipitation case. After checking its good behavior on artificial data, the proposed post-processing technique is applied to temperature and precipitation e

关键词： Hierarchical latent variable models em algorithms Ensemble numerical weather prediction Statistical post-processing Temperature Precipitation

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