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Groundwater pollution source identification using metropolis-hasting algorithm combined with Kalman filter algorithm

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JOURNAL OF HYDROLOGY 2023年第PartA期626卷

作者： Luo, Jiannan Li, Xueli Xiong, Yu Liu, Yong Jilin Univ Key Lab Groundwater Resources & Environm Minist Educ Changchun 130021 Peoples R China Jilin Univ Jilin Prov Key Lab Water Resources & Environm Changchun 130021 Peoples R China Jilin Univ Coll New Energy & Environm Changchun 130021 Peoples R China

Increasing the precision of groundwater pollution source identification (GPSI) is crucial for groundwater pollution control and risk management. Bayesian theory based on the Markov Chain Monte Carlo (MCMC) method is a useful strategy of solving the GPSI problem. However, because of the nonlinear and uncertainty characteristics of GPSI, the metropolis-hasting (MH) algorithm, one of the most well-known MCMC algorithms, has the disadvantage of relatively low precision and is time-consuming. To address this problem, the Kalman filter (KF) algorithm was combined with the MH algorithm and referred to as the Kalman filter metropolishasting (KF-MH) algorithm. The algorithm generates a new initial distribution that is close to the true value through a prior distribution, and the new initial distribution is used to perform subsequent iterations of the calculation. The viability and superiority of the proposed KF-MH algorithm were assessed in three hypothetical GPSI cases under different conditions. In the inversion process, a surrogate model was constructed using a temporal convolutional network (TCN) to reduce the computational pressure imposed by the numerical simulation model. The results of the TCN surrogate model in the cases illustrate the high accuracy of the TCN surrogate model in fitting the groundwater numerical model. In the three cases, the normalized errors between the identification results and the true values of the source features obtained with the KF-MH algorithm were significantly lower than those of the MH algorithm. The results indicate that the proposed KF-MH algorithm has higher inversion accuracy than the MH algorithm.

关键词： Groundwater pollution source Temporal convolutional network Surrogate model metropolis-hasting algorithm Kalman filter algorithm

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Analysis of unit-Weibull based on progressive type-II censored with optimal scheme

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ALEXANDRIA ENGINEERING JOURNAL 2023年 63卷 321-338页

作者： Almetwally, Ehab M. Jawa, Taghreed M. Sayed-Ahmed, Neveen Park, Choonkil Zakarya, Mohammed Dey, Sanku Delta Univ Sci & Technol Fac Business Adm Gamasa 11152 Egypt Sci Assoc Studies & Appl Res SASAR Al Manzalah Egypt Taif Univ Coll Sci Dept Math & Stat POB 11099 Taif 21944 Saudi Arabia Hanyang Univ Res Inst Nat Sci Seoul 04763 South Korea King Khalid Univ Coll Sci Dept Math POB 9004 Abha 61413 Saudi Arabia Al Azhar Univ Fac Sci Dept Math Assiut 71524 Egypt St Anthonys Coll Dept Stat Shillong Meghalaya India

Using progressive Type-II censoring data, this study deals with the estimation of param-eters of the Unit-Weibull distribution using two classical methods and the Bayesian method. In the classical methods, maximum likelihood and the maximum product of spacing (MPS) methods are used to obtain the parameters of the model by utilizing the Newton-Raphson method. On the basis of observed Fisher information matrix, approximate confidence intervals for the unknown param-eters are obtained. In addition, two bootstrap methods are used to obtain confidence intervals for the unknown parameters of the model. In the Bayesian estimation, we have considered both like-lihood function as well as product of spacing function to estimate the model parameters. Bayes esti-mators are obtained under squared error loss function using independent gamma density priors for the unknown model parameters. Since closed-form of the Bayes estimators is not available, the metropolis-hastings algorithm is proposed to approximate the Bayes estimates. In addition, high-est posterior density credible intervals are obtained. Further, using different optimally criteria, an optimal scheme has been proposed. A simulation study is conducted to assess the statistical perfor-mance of all the estimators. To demonstrate the proposed methodology a real data analysis is pro-vided to illustrate all the statistical inferential procedures developed in the paper.(c) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY license (http://***/licenses/by/ 4.0/).

关键词： Progressive Type-II censoring Bayes estimator Bootstrapping metropolis-hasting algorithm optimality

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Reliability characteristics of COVID-19 death rate using generalized progressive hybrid censored data

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International Journal of Quality and Reliability Management 2024年第3期41卷 850-878页

作者： Irfan, Mohd Sharma, Anup Kumar Department of Mathematics National Institute of Technology Raipur Raipur India

Purpose: A progressive hybrid censoring scheme (PHCS) becomes impractical for ensuring dependable outcomes when there is a low likelihood of encountering a small number of failures prior to the predetermined terminal time T. The generalized progressive hybrid censoring scheme (GPHCS) efficiently addresses to overcome the limitation of the PHCS. Design/methodology/approach: In this article, estimation of model parameter, survival and hazard rate of the Unit-Lindley distribution (ULD), when sample comes from the GPHCS, have been taken into account. The maximum likelihood estimator has been derived using Newton–Raphson iterative procedures. Approximate confidence intervals of the model parameter and their arbitrary functions are established by the Fisher information matrix. Bayesian estimation procedures have been derived using metropolis–hastings algorithm under squared error loss function. Convergence of Markov chain Monte Carlo (MCMC) samples has been examined. Various optimality criteria have been considered. An extensive Monte Carlo simulation analysis has been shown to compare and validating of the proposed estimation techniques. Findings: The Bayesian MCMC approach to estimate the model parameters and reliability characteristics of the generalized progressive hybrid censored data of ULD is recommended. The authors anticipate that health data analysts and reliability professionals will get benefit from the findings and approaches presented in this study. Originality/value: The ULD has a broad range of practical utility, making it a problem to estimate the model parameters as well as reliability characteristics and the significance of the GPHCS also encourage the authors to consider the present estimation problem because it has not previously been discussed in the literature. © 2023, Emerald Publishing Limited.

关键词： Bayesian estimation Coverage probability Delta method Generalized progressive hybrid censoring scheme MCMC convergence metropolis-hasting algorithm Optimality Relative absolute bias Root mean square error Unit Lindley distribution

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The Pareto-Poisson Distribution: Characteristics, Estimations and Engineering Applications

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SANKHYA-SERIES A-MATHEMATICAL STATISTICS AND PROBABILITY 2023年第1期85卷 1058-1099页

作者： Elshahhat, Ahmed El-Sherpieny, EL-Sayed A. Hassan, Amal S. Zagazig Univ Fac Technol & Dev Zagazig 44519 Egypt Cairo Univ Fac Grad Studies Stat Res Giza 12613 Egypt

A new three-parameter lifetime distribution based on compounding Pareto and Poisson distributions is introduced and discussed. Various statistical and reliability properties of the proposed distribution including: quantiles, ordinary moments, median, mode, quartiles, mean deviations, cumulants, generating functions, entropies, mean residual life, order statistics and stress-strength reliability are obtained. In presence of data collected under Type-II censoring, from frequentist and Bayesian points of view, the model parameters are estimated. Using independent gamma priors, Bayes estimators against the squared-error, linear-exponential and general-entropy loss functions are developed. Based on asymptotic properties of the classical estimators, asymptotic confidence intervals of the unknown parameters are constructed using observed Fisher's information. Since the Bayes estimators cannot be obtained in closed-form, Markov chain Monte Carlo techniques are considered to approximate the Bayes estimates and to construct the highest posterior density intervals. A Monte Carlo simulation study is conducted to examine the performance of the proposed methods using various choices of effective sample size. To highlight the perspectives of the utility and flexibility of the new distribution, two numerical applications using real engineering data sets are investigated and showed that the proposed model fits well compared to other eleven lifetime models.

关键词： Pareto-Poisson distribution classical and Bayesian estimators Gelman and Rubin's diagnostic hazard rate function type-II censoring metropolis-hasting algorithm

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A change-time hazard rate model and its goodness of fit

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INTERNATIONAL JOURNAL OF SYSTEM ASSURANCE ENGINEERING AND MANAGEMENT 2022年第4期13卷 1903-1912页

作者： Singh, Bhupendra Rathi, Shubhi Singh, Gajraj Gupta, Puneet Kumar CCS Univ Dept Stat Meerut Uttar Pradesh India ICFAI Univ ICFAI Business Sch Dehra Dun Uttarakhand India

The study presents the estimation of the location of the change in the hazard-rate function of the survival times of patients who continue to live after a major life-threatening medical operation. The real data set that acts as a backbone for the present work is the Stanford heart transplantation data. On studying and interpreting, the non-parametric hazard rate plot, and cumulative hazard curve of the data, a suitable hazard rate model is proposed. The parameters involved in the proposed model have been assessed by the classical and Bayesian methods estimation. The likelihood-ratio test has been conducted to test the validity of the change time point in the data.

关键词： Change-time hazard-rate model Cumulative hazard function Survival function metropolis-hasting algorithm Gibbs sample

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Most Likely Optimal Subsampled Markov Chain Monte Carlo

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Journal of Systems Science & Complexity 2021年第3期34卷 1121-1134页

作者： HU Guanyu WANG Haiying University of Missouri-Columbia USA University of Connecticut USA

Markov Chain Monte Carlo(MCMC) requires to evaluate the full data likelihood at different parameter values iteratively and is often computationally infeasible for large data sets. This paper proposes to approximate the log-likelihood with subsamples taken according to nonuniform subsampling probabilities, and derives the most likely optimal(MLO) subsampling probabilities for better approximation. Compared with existing subsampled MCMC algorithm with equal subsampling probabilities,the MLO subsampled MCMC has a higher estimation efficiency with the same subsampling ratio. The authors also derive a formula using the asymptotic distribution of the subsampled log-likelihood to determine the required subsample size in each MCMC iteration for a given level of precision. This formula is used to develop an adaptive version of the MLO subsampled MCMC algorithm. Numerical experiments demonstrate that the proposed method outperforms the uniform subsampled MCMC.

关键词： Big data MCMC metropolis-hasting algorithm nonuniform subsampling

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Bayesian survival analysis for adaptive Type-II progressive hybrid censored Hjorth data

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COMPUTATIONAL STATISTICS 2021年第3期36卷 1965-1990页

作者： Elshahhat, Ahmed Nassar, Mazen Zagazig Univ Fac Technol & Dev Dept Accounting & Quantitat Informat Syst Zagazig Egypt King Abdulaziz Univ Fac Sci Dept Stat Jeddah Saudi Arabia

Adaptive Type-II progressive hybrid censoring scheme has been proposed to increase the efficiency of statistical analysis and save the total test time on a life-testing experiment. This article deals with the problem of estimating the parameters, survival and hazard rate functions of the two-parameter Hjorth distribution under adaptive Type-II progressive hybrid censoring scheme using maximum likelihood and Bayesian approaches. The two-sided approximate confidence intervals of the unknown quantities are constructed. Under the assumption of independent gamma priors, the Bayes estimators are obtained using squared error loss function. Since the Bayes estimators cannot be expressed in closed forms, Lindley's approximation and Markov chain Monte Carlo methods are considered and the highest posterior density credible intervals are also obtained. To study the behavior of the various estimators, a Monte Carlo simulation study is performed. The performances of the different estimators have been compared on the basis of their average root mean squared error and relative absolute bias. Finally, to show the applicability of the proposed estimators a data set of industrial devices has been analyzed.

关键词： Adaptive Type-II progressive hybrid censoring scheme Bayes estimator metropolis-hasting algorithm Hjorth distribution Lindley’ s approximation method Maximum likelihood estimator Reliability characteristics

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Polya tree Monte Carlo method

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2023年 180卷

作者： Zhuang, Haoxin Diao, Liqun Yi, Grace Y. Univ Waterloo Dept Stat & Actuarial Sci 200 Univ Ave West Waterloo ON N2L 3G1 Canada Univ Western Ontario Dept Stat & Actuarial Sci Dept Comp Sci 1151 Richmond St London ON N6A 5B7 Canada

Markov Chain Monte Carlo (MCMC) methods have been widely used in Statistics and ma-chine learning research. However, such methods have several limitations, including slow convergence and the inefficiency in handling multi-modal distributions. To overcome these limitations of MCMC methods, a new, efficient sampling method has been proposed and it applies to general distributions including multi-modal ones or those having complex struc-ture. The proposed approach, called the Polya tree Monte Carlo (PTMC) method, roots in constructing a Polya tree distribution using the idea of Monte Carlo method, and then using this distribution to approximate and facilitate sampling from a target distribution that may be complex or have multiple modes. The associated convergence property of the PTMC method is established and computationally efficient sampling algorithms are developed based on the PTMC. Extensive numerical studies demonstrate the satisfactory performance of the proposed method under various settings including its superiority to the usual MCMC algorithms. The evaluation and comparison are carried out in terms of sampling efficiency, computational speed and the capacity of identifying distribution modes. Additional details about the method, proofs and simulation results are provided in the Supplementary Web Appendices online. (c) 2022 Elsevier B.V. All rights reserved.

关键词： Gibbs sampler Markov Chain Monte Carlo metropolis-hasting algorithm Polya trees Sampling from a distribution

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Optimal analysis of adaptive type-II progressive censored for new unit-lindley model

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JOURNAL OF KING SAUD UNIVERSITY SCIENCE 2023年第2期35卷

作者： Alrumayh, Amani Weera, Wajaree Khogeer, Hazar A. Almetwally, Ehab M. Northern Border Univ Coll Sci Dept Math Ar Ar Saudi Arabia Khon Kaen Univ Fac Sci Dept Math Khon Kaen 40002 Thailand Umm Al Qura Univ Coll Appl Sci Dept Math Sci Mecca Saudi Arabia Delta Univ Sci & Technol Fac Business Adm Gamasa 11152 Egypt Sci Assoc Studies & Appl Res Al Manzalah 35646 Egypt

The parameters, reliability, and hazard rate functions of the Unit-Lindley distribution based on adaptive Type-II progressive censored sample are estimated using both non-Bayesian and Bayesian inference methods in this study. The Newton-Raphson method is used to obtain the maximum likelihood and maximum product of spacing estimators of unknown values in point estimation. On the basis of observable Fisher information data, estimated confidence ranges for unknown parameters and reliability characteristics are created using the delta approach and the frequentist estimators' asymptotic normality approximation. To approximate confidence intervals, two bootstrap approaches are utilized. Using an independent gamma density prior, a Bayesian estimator for the squared-error loss is derived. The metropolis-hastings algorithm is proposed to approximate the Bayesian estimates and also to create the associated highest posterior density credible intervals. Extensive Monte Carlo simulation tests are carried out to evaluate the performance of the developed approaches. For selecting the optimum progressive censoring scheme, several optimality criteria are offered. A practical case based on COVID-19 data is used to demonstrate the applicability of the presented methodologies in real-life COVID-19 scenarios. (c) 2022 The Author(s). Published by Elsevier B.V. on behalf of King Saud University.

关键词： Adaptive Type -II progressive censoring Bayesian estimator Bootstrapping metropolis-hasting algorithm Reliability Unit -Lindley distribution

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Estimation of Parameters of the GIE Distribution Under Progressive Type-I Censoring

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JOURNAL OF STATISTICAL THEORY AND APPLICATIONS 2021年第2期20卷 380-394页

作者： Mahmoud, Mahmoud R. Muhammed, Hiba Z. El-Saeed, Ahmed R. Abdellatif, Ashraf D. Cairo Univ Fac Grad Studies Stat Res Dept Math Stat Giza Egypt Obour High Inst Management & Informat Dept Basic Sci Al Obour City Egypt Higher Technol Inst Dept Technol Management & Informat 10th Of Ramadan City Egypt

In this paper, we consider generalized inverted exponential distribution which is capable of modeling various shapes of failure rates and aging processes. Based on progressive Type-I censored data, we consider the problem of estimation of parameters under classical and Bayesian approaches. In this regard, we obtain maximum likelihood estimates and Bayes estimates under squared error loss function. We also compute a 95% asymptotic confidence interval, bootstrap confidence intervals and highest posterior density (HPD) credible interval estimates. Finally, we analyze a real data set and conduct a Monte Carlo simulation study to compare the performance of the various proposed estimators. (C) 2021 The Authors. Published by Atlantis Press B.V.

关键词： Generalized inverted exponential distribution Progressive Type-I censoring scheme Maximum likelihood estimation Bayesian estimation Markov chain Monte Carlo metropolis-hasting algorithm

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