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A novel approach for modelling pattern and spatial dependence structures between climate variables by combining mixture models with copula models

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INTERNATIONAL JOURNAL OF CLIMATOLOGY 2020年第2期40卷 1049-1066页

作者： Khan, Firdos Spoeck, Gunter Pilz, Juergen Natl Univ Sci & Technol Sch Nat Sci Islamabad 44000 Pakistan Alpen Adria Univ Inst Stat Klagenfurt Austria

Spatiotemporal dependence structures play a pivotal role in understanding the meteorological characteristics of a basin or subbasin. This further affects the hydrological conditions and, consequently, will provide misleading results if these structures are not taken into account properly. In this study, we modelled the spatial dependence structure of three climate variables, maximum and minimum temperature and precipitation, throughout the Monsoon-dominated zone of Pakistan. For temperature, six meteorological stations have been considered, for precipitation we used the results of four meteorological stations. For modelling the dependence structure between temperature and precipitation at multiple sites, we utilized C-Vine, D-Vine and student t-copula models. For temperature, multivariate mixture normal distributions, and for precipitation, the gamma distribution, have been used as marginals under the copula models. The models were calibrated by utilizing the 20 years daily data from 1981 to 2000, and for validation, we used the data for 10-year period from 2001 to 2010. The simulations were performed for each variable separately, conditioned on spatial neighbours. A comparison was made between the different copula models, on the basis of observational and simulated patterns and spatial dependence structures, the performance was evaluated for the validation period. The results show that all copula models performed well;however, there are subtle differences between them. The copula models captured the patterns and spatial dependence structures between climate variables, however, the t-copula showed poor performance in reproducing the dependence structure with respect to magnitude. It was observed that important statistics of observed data have been closely approximated except a few maximum values for maximum temperature and minimum values for minimum temperature. Probability density functions of simulated data follow closely the pattern of observational data. These m

关键词： copula model C-Vine D-Vine em algorithm mixture models monsoon spatial dependence structure

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A general method of computing mixed Poisson probabilities by Monte Carlo sampling

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MATHemATICS AND COMPUTERS IN SIMULATION 2020年 170卷 98-106页

作者： Ong, Seng-Huat Lee, Wen-Jau Low, Yeh-Ching UCSI Univ Dept Actuarial Sci & Appl Stat Kuala Lumpur 56000 Malaysia Suntech Penang Cybercity Invantest DSG Lintang Mayang Pasir 3 Bayan Baru 11950 Pulau Pinang Malaysia Sunway Univ Dept Comp & Informat Syst Petaling Jaya 47500 Selangor Malaysia

Mixed Poisson distributions form an important class of distributions in applications. However, the application of many of these mixed Poisson distributions is hampered by the complicated probability distributions. The paper examines Monte Carlo sampling as a general technique for computation of mixed Poisson probabilities which is applicable to any mixed Poisson distribution with arbitrary mixing distribution. The accuracy and computational speed of this method is illustrated with the Poisson-inverse Gaussian distribution. The proposed method is then applied to compute probabilities of the Poisson-lognormal distribution, a popular species abundance model. It is also shown that in the maximum likelihood estimation of Poisson-lognormal parameters by E-M algorithm, the application of the proposed Monte Carlo computation in the algorithm avoids numerical problems. (C) 2019 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

关键词： Gamma distribution Poisson-lognormal Species abundance Variance reduction Quasi-Monte Carlo em algorithm

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Robust Segmentation Based on Salient Region Detection Coupled Gaussian Mixture Model

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INFORMATION 2022年第2期13卷 98页

作者： Pan, Xiaoyan Zheng, Yuhui Jeon, Byeungwoo Nanjing Univ Informat Sci & Technol Sch Comp & Software Nanjing 210044 Peoples R China Sungkyunkwan Univ Sch Elect & Elect Engn Suwon 440746 South Korea

The impressive progress on image segmentation has been witnessed recently. In this paper, an improved model introducing frequency-tuned salient region detection into Gaussian mixture model (GMM) is proposed, which is named FTGMM. Frequency-tuned salient region detection is added to achieve the saliency map of the original image, which is combined with the original image, and the value of the saliency map is added into the Gaussian mixture model in the form of spatial information weight. The proposed method (FTGMM) calculates the model parameters by the expectation maximization (em) algorithm with low computational complexity. In the qualitative and quantitative analysis of the experiment, the subjective visual effect and the value of the evaluation index are found to be better than other methods. Therefore, the proposed method (FTGMM) is proven to have high precision and better robustness.

关键词： image segmentation salient region detection Gaussian mixture model em algorithm

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Image patch prior learning based on random neighbourhood resampling for image denoising

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IET IMAGE PROCESSING 2020年第5期14卷 838-844页

作者： Ji, Jian Wei, Jiajie Fan, Guoliang Bai, Mengqi Huang, Jingjing Miao, Qiguang Xidian Univ Sch Comp Sci & Technol Xian 710071 Peoples R China Oklahoma State Univ Sch Elect & Comp Engn Stillwater OK 74078 USA

Image patch priors become a popular tool for image denoising. The Gaussian mixture model (GMM) is remarkably effective in modelling natural image patches. However, GMM prior learning using the expectation maximisation (em) algorithm is sensitive to the initialisation, often leading to low convergence rate of parameter estimation. In this study, a novel sampling method called random neighbourhood resampling (RNR) is proposed to improve the accuracy and efficiency of parameter estimation. An enhanced GMM (EGMM) learning algorithm is further developed by incorporating RNR into the em algorithm to initialise and update the GMM prior. The learned EGMM prior is applied in the expected patch log-likelihood (EPLL) framework for image denoising. The effectiveness and performance of the proposed RNR and EGMM algorithm are demonstrated via extensive experimental results comparing with the state-of-the-art image denoising methods, the experimental results show the higher PSNR result of the denoised images using the proposed method. Meanwhile, the authors verified that the proposed method can efficiently reduce the time of image denoising compared with the basic EPLL method.

关键词： image denoising mixture models learning (artificial intelligence) Gaussian processes expectation-maximisation algorithm random neighbourhood resampling Gaussian mixture model natural image patches expectation maximisation algorithm parameter estimation RNR enhanced GMM learning algorithm expected patch log-likelihood framework EGMM algorithm image denoising methods image patch prior learning em algorithm EPLL framework

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Robust Task Learning Based on Nonlinear Regression With Mixtures of Student-<italic>t</italic>Distributions

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IEEE ACCESS 2020年 8卷 109835-109844页

作者： Cao, Chunzheng Wang, Ziyue Shi, Jian Qing Chen, Yunjie Nanjing Univ Informat Sci & Technol Sch Math & Stat Nanjing 210044 Peoples R China Newcastle Univ Sch Math Stat Newcastle Upon Tyne NE1 7RU Tyne & Wear England

We propose a robust task learning method based on nonlinear regression model with mixtures of -distributions. The model can adaptively reduce the effects of complex noises and accurately learn the nonlinear structure of targets. By introducing latent variables, the model is expressed into a hierarchical structure, which helps explain the advantage of flexibility compared to the traditional Gaussian based learning model. We develop a two-stage efficient estimation procedure to obtain penalized likelihood estimator of the parameters combined an expectation-maximization algorithm with Lagrange multiplier method. The learning performances of the model are investigated through experiments on both synthetic and real data sets.

关键词： Task analysis Adaptation models Kernel Optimization Gaussian distribution Data models Robustness Task learning robust nonlinear regression outlier em algorithm kernel method

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Dynamic Bayesian network for crop growth prediction in greenhouses

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COMPUTERS AND ELECTRONICS IN AGRICULTURE 2020年 169卷 105167-105167页

作者： Kocian, A. Massa, D. Cannazzaro, S. Incrocci, L. Di Lonardo, S. Milazzo, P. Chessa, S. Pisa Univ Dept Comp Sci Pisa Italy Pisa Univ Dept Agr Food & Evironmen4 Pisa Italy Council Agr Res & Econ Res Ctr Vegetable & Ornamental Crops Pescia Italy CNR IRET Natl Res Council Res Inst Terr Ecosyst Florence Italy

The paper presents an Internet-of-Things based agricultural decision support system for crop growth. A dynamic Bayesian network (DBN) relates indicative parameters of crop development to environmental control parameters via unobserved (hidden) Markov states. The expectation-maximization algorithm is used to track the states and to learn the parameters of the DBN. The steady state information is then used to derive a predictor for the measurement data a few days ahead. The proposed DBN avoids time-consuming training cultivation cycles, as only data of the current cultivation cycle are available to the algorithm. Three cultivation cycles of lettuce have been used to test the performance of the proposed DBN. The environmental parameters were temperature, solar irradiance and vapor-pressure deficit. The measurement data include evapotranspiration at granularity equal one day, and leaf-area index and dry weight, at granularity equal one week. It turned out that accurate measurement data prediction a few days ahead is possible even if the number of data samples is low.

关键词： Internet of Things Evapotranspiration Leaf-area em algorithm Prediction

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Finite mixture model of hidden Markov regression with covariate dependence

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STAT 2022年第1期11卷

作者： Sarkar, Shuchismita Zhu, Xuwen Bowling Green State Univ Dept Appl Stat & Operat Res Bowling Green OH 43403 USA Univ Alabama Dept Informat Syst Stat & Management Sci Tuscaloosa AL USA

In recent days, a combination of finite mixture model (FMM) and hidden Markov model (HMM) is becoming popular for partitioning heterogeneous temporal data into homogeneous groups (clusters) with homogeneous time points (regimes). The regression mixtures commonly considered in this approach can also accommodate for covariates present in data. The classical fixed covariate approach, however, may not always serve as a reasonable assumption as it is incapable of accounting for the contribution of covariates in cluster formation. This paper introduces a novel approach for detecting clusters and regimes in time series data in the presence of random covariates. The computational challenges related to the proposed model has been discussed, and several simulation studies are performed. An application to United States COVID-19 data yields meaningful clusters and regimes.

关键词： em algorithm finite mixture model hidden Markov model model based clustering regime change

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Timely epidemic monitoring in the presence of reporting delays: anticipating the COVID-19 surge in New York City, September 2020

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BMC PUBLIC HEALTH 2022年第1期22卷 871-871页

作者： Harris, Jeffrey E. MIT 77 Massachusetts Ave Cambridge MA 02139 USA Eisner Hlth Los Angeles CA 90015 USA

Background During a fast-moving epidemic, timely monitoring of case counts and other key indicators of disease spread is critical to an effective public policy response. Methods We describe a nonparametric statistical method, originally applied to the reporting of AIDS cases in the 1980s, to estimate the distribution of reporting delays of confirmed COVID-19 cases in New York City during the late summer and early fall of 2020. Results During August 15-September 26, the estimated mean delay in reporting was 3.3 days, with 87% of cases reported by 5 days from diagnosis. Relying upon the estimated reporting-delay distribution, we projected COVID-19 incidence during the most recent 3 weeks as if each case had instead been reported on the same day that the underlying diagnostic test had been performed. Applying our delay-corrected estimates to case counts reported as of September 26, we projected a surge in new diagnoses that had already occurred but had yet to be reported. Our projections were consistent with counts of confirmed cases subsequently reported by November 7. Conclusion The projected estimate of recently diagnosed cases could have had an impact on timely policy decisions to tighten social distancing measures. While the recent advent of widespread rapid antigen testing has changed the diagnostic testing landscape considerably, delays in public reporting of SARS-CoV-2 case counts remain an important barrier to effective public health policy.

关键词： SARS-CoV-2 Coronavirus Reporting delays em algorithm Voluntary testing Epidemic surveillance Nonparametric estimation Molecular diagnostic tests Rapid diagnostic tests

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Variational-Based Mixed Noise Removal With CNN Deep Learning Regularization

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IEEE TRANSACTIONS ON IMAGE PROCESSING 2020年 29卷 1246-1258页

作者： Wang, Faqiang Huang, Haiyang Liu, Jun Beijing Normal Univ Sch Math Sci Minist Educ China Lab Math & Complex Syst Beijing 100875 Peoples R China

In this paper, the traditional model based variational methods and deep learning based algorithms are naturally integrated to address mixed noise removal, specially for Gaussian mixture noise and Gaussian-impulse noise removal problem. To be different from single type noise (e.g. Gaussian) removal, it is a challenge problem to accurately discriminate noise types and levels for each pixel. We propose a variational method to iteratively estimate the noise parameters, and then the algorithm can automatically classify the noise according to the different statistical parameters. The proposed variational problem can be separated into regularization, synthesis, parameters estimation and noise classification four steps with the operator splitting scheme. Each step is related to an optimization subproblem. To enforce the regularization, the deep learning method is employed to learn the natural images prior. Compared with some model based regularizations, the CNN regularizer can significantly improve the quality of the restored images. Compared with some learning based methods, the synthesis step can produce better reconstructions by analyzing the types and levels of the recognized noise. In our method, the convolution neutral network (CNN) can be regarded as an operator which associated to a variational functional. From this viewpoint, the proposed method can be extended to many image reconstruction and inverse problems. Numerical experiments in the paper show that our method can achieve some state-of-the-art results for Gaussian mixture noise and Gaussian-impulse noise removal.

关键词： Deep learning Noise reduction Image restoration Learning systems TV Data models Deep learning CNN regularization mixed noise em algorithm image restoration

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Statistical analysis of longitudinal studies

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INTERNATIONAL STATISTICAL REVIEW 2022年第Sup1期90卷 S2-S16页

作者： Laird, Nan M. Harvard TH Chan Sch Publ Hlth Dept Biostat Boston MA 02115 USA

Longitudinal studies play a prominent role in research on growth, change and/or decline in individuals, and in characterising the environmental and social factors which influence change. The essential feature of a longitudinal study is taking repeated measures of an outcome on the same set of individuals at multiple timepoints, thereby allowing investigators to characterise within subject changes during the measurement period. This paper provides an overview of how the basic design features and analysis of longitudinal studies are related to other study designs, including longitudinal clinical trials as well as repeated measures studies. I summarise the use of the linear mixed model as described in Laird and Ware for the analysis of a broad class of designs and present some applications in health and medicine.

关键词： em algorithm linear mixed model random effects studies of growth and change

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