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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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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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INVERSE PROBLEM FOR ELECTROMAGNETIC PROPAGATION IN A DIELECTRIC MEDIUM USING MARKOV CHAIN MONTE CARLO METHOD

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INTERNATIONAL JOURNAL OF INNOVATIVE COMPUTING INFORMATION AND CONTROL 2012年第3B期8卷 2339-2346页

作者： Kojima, Fumio Knopp, Jeremy S. Kobe Univ Org Adv Sci & Technol Nada Ku Kobe Hyogo 6578501 Japan USAF AFRL RXLP Nondestruct Evaluat Branch Res Lab Wright Patterson AFB OH 45433 USA

This paper is concerned with a stochastic inverse methodology arising in electromagnetic imaging. Nondestructive testing using guided microwaves covers a wide range of industrial applications including early detection of anomalies in conducting materials. The focus of this paper is the identification of electromagnetic material parameters and emphasis is on one dimensional scattering of a dielectric slab. The direct problem can be solved numerically using the finite-difference time-domain method (FDTD). The Markov Chain Monte Carlo method (MCMC) is applied to the inversion problem. Some successful results of computational experiments are demonstrated in order to show the feasibility and applicability of the proposed method.

关键词： Microwave Dielectric loss Electrical cable FDTD metropolis-hasting algorithm

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Inversely estimating temperature sensitivity of soil carbon decomposition by assimilating a turnover model and long-term field data

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SOIL BIOLOGY & BIOCHEMISTRY 2012年 46卷 191-199页

作者： Sakurai, Gen Jomura, Mayuko Yonemura, Seiichiro Iizumi, Toshichika Shirato, Yasuhito Yokozawa, Masayuki Natl Inst Agroenvironm Sci Tsukuba Ibaraki 3058604 Japan Nihon Univ Coll Bioresources Sci Fujisawa Kanagawa 2520880 Japan

Change in temperature sensitivity of soil organic carbon (SOC) decomposition with change in soil qualities (i.e. decomposability or lability) is one of the most important issues to be evaluated for projection of future CO2 emissions from soils. We inversely estimated the temperature sensitivity of SOC decomposition rate by applying a hybrid of the metropolis-hasting algorithm and the particle filter method to the extended Rothamsted carbon model (RothC), together with long-term (9 years) experimental data on SOC obtained at five sites in Japanese upland soils. Contrary to the prediction of the Arrhenius kinetics theory, we found no significant differences in temperature sensitivity among soils with different qualities (represented as soil compartments in the RothC model). We also confirmed that there was a positive correlation between the relative temperature sensitivity of the humus compartment and future total CO2 emissions. The RothC model with default parameterization tended to overestimate future total CO2 emissions relative to the calibrated model, and the degree of overestimation was larger than that of underestimation. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Soil organic carbon Decomposition rate Temperature sensitivity Turnover model Long-term field experiment Data assimilation Particle filter metropolis-hasting algorithm

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A simulated annealing algorithm for the creation of synthetic population in activity-based travel demand model

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KSCE JOURNAL OF CIVIL ENGINEERING 2016年第6期20卷 2513-2523页

作者： Kim, Jooyoung Lee, Seungjae Univ Seoul Integrated Urban Res Ctr Seoul 02504 South Korea Univ Seoul Dept Transportat Engn Seoul 02504 South Korea

Synthetic population serves as an agent group of the population of activity patterns that possesses identical socio-economic characteristics applied on the model that forecasts the travel demand in the activity-based profile. During the development of agentbased traffic simulation model, the accuracy of simulation outcomes relies highly on population synthesis. This study endeavors to develop a synthetic population, based on the Simulated Annealing (SA) algorithm for the activity-based travel demand model. Hill climbing and cooling schedule are essential elements to be considered when applying SA into the synthetic population. Also, metropolis-hasting algorithm was employed to decide whether to select or dismiss the follow-up distribution so that hill climbing phenomenon can be prevented. Additionally, the stability of the algorithm was figured through a scenario analysis of the optimal combination of iteration and temperature T on cooling issue. On the basis of this result, the current condition of micro sample and census data were utilized to compare the IPF (Iterative Proportional Fitting) of previous methodology with the establishment result of suggested algorithm. It is found that the algorithm is valid and built with the synthetic population based on SA through statistical verification. It is resulted from the application of the suggested SA method that such tradition algorithm as IPF has zero-cell or sample biased problems. However, not only can SA algorithm overcome such problems but also it can effectively address hill climbing and cooling schedule issues.

关键词： synthetic population simulated annealing iterative proportional fitting metropolis-hasting algorithm activity-based simulation

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Modified Hamiltonian Monte Carlo-based Bayesian finite element model updating of steel truss bridge

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STRUCTURAL CONTROL & HEALTH MONITORING 2020年第8期27卷 e2556-e2556页

作者： Baisthakur, Shubham Chakraborty, Arunasis Indian Inst Technol Dept Civil Engn Gauhati India

The aim of this study is to develop a Hamiltonian Monte Carlo-based algorithm for finite element model updating in the Bayesian framework. The proposed algorithm uses adaptive prior-based approach, which helps to generate the intermediate pdfs. Numerical analysis is carried out with different coefficient of variations of the prior for model updating. Guidelines for their proper selection procedure are also prescribed in this work. The efficiency of the proposed method is demonstrated using synthetic experiments and actual test data for updating the finite element model of a steel truss bridge. Finally, performance of this algorithm is compared with the standard Markov chain Monte Carlo algorithm to demonstrate its advantages.

关键词： Bayesian inference maximum likelihood metropolis-hasting algorithm model updating modified Hamiltonian Monte Carlo simulation

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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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Graph_sampler: a simple tool for fully Bayesian analyses of DAG-models

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COMPUTATIONAL STATISTICS 2017年第2期32卷 691-716页

作者： Datta, Sagnik Gayraud, Ghislaine Leclerc, Eric Bois, Frederic Y. Univ Technol Compiegne Sorbonne Univ BMBI Bat GICS 60 319 F-60203 Compiegne France Univ Technol Compiegne Sorbonne Univ LMAC Bat GICS 60 319 F-60203 Compiegne France Univ Tokyo LIMMS CNRS IIS UMI 2820 Inst Ind Sci Meguro Ku 4-6-1 Komaba Tokyo 1538505 Japan INERIS DRC VIVA METO Parc ALATA BP2 F-60550 Verneuil En Halatte France

Bayesian networks (BNs) are widely used graphical models usable to draw statistical inference about directed acyclic graphs. We presented here Graph_sampler a fast free C language software for structural inference on BNs. Graph_sampler uses a fully Bayesian approach in which the marginal likelihood of the data and prior information about the network structure are considered. This new software can handle both the continuous as well as discrete data and based on the data type two different models are formulated. The software also provides a wide variety of structure prior which can depict either the global or local properties of the graph structure. Now based on the type of structure prior selected, we considered a wide range of possible values for the prior making it either informative or uninformative. We proposed a new and much faster jumping kernel strategy in the metropolis-hastings algorithm. The source C code distributed is very compact, fast, uses low memory and disk storage. We performed out several analyses based on different simulated data sets and synthetic as well as real networks to discuss the performance of Graph_sampler.

关键词： Bayesian networks Structure learning Posterior distribution MCMC metropolis-hasting algorithm

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A Short History of Markov Chain Monte Carlo: Subjective Recollections from Incomplete Data

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STATISTICAL SCIENCE 2011年第1期26卷 102-115页

作者： Robert, Christian Casella, George Univ Paris 09 CEREMADE F-75785 Paris 16 France Univ Florida Dept Stat Gainesville FL 32611 USA

We attempt to trace the history and development of Markov chain Monte Carlo (MCMC) from its early inception in the late 1940s through its use today. We see how the earlier stages of Monte Carlo (MC, not MCMC) research have led to the algorithms currently in use. More importantly, we see how the development of this methodology has not only changed our solutions to problems, but has changed the way we think about problems.

关键词： Gibbs sampling metropolis-hasting algorithm hierarchical models Bayesian methods

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Bayesian methods applied to survey data from archeological magnetometry

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2001年第453期96卷 64-76页

作者： Aykroyd, RG Haigh, JGB Allum, GT Univ Leeds Dept Stat Leeds LS2 9JT W Yorkshire England Univ Bradford Dept Math Bradford BD7 1DP W Yorkshire England

A model is presented for the interpretation of magnetometer data in terms of archeological features beneath the ground. it describes the detector's response to the assemblage of buried features, incorporating both a spread function and a statistical error process as well as appropriate prior beliefs about the nature of archeological features. The problem is to estimate the magnetic susceptibility of the buried features at each horizontal location. A Monte Carlo Markov chain approach is used to estimate magnetic susceptibilities and all prior parameters. This requires estimation of the normalization constant of the Gibbs prior distribution. The approach is illustrated with both simulated data and measurements from an archeological rite. In the latter case, the reconstruction of the buried features corresponds well with the archeologist's observations during subsequent excavation.

关键词： archeology geophysics image reconstruction inverse data problems metropolis-hasting algorithm Monte Carlo Markov chain normalizing constant

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