• Journal of the Computational Structural Engineering Institute of Korea
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• v.36 no.3
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• pp.203-211
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• 2023

A Markov chain Monte Carlo (MCMC) simulation is proposed for probabilistic full waveform inversion (FWI) in a layered half-space. Dynamic responses on the half-space surface are estimated using the thin-layer method when a harmonic vertical force is applied. Subsequently, a posterior probability distribution function and the corresponding objective function are formulated to minimize the difference between estimations and observed data as well as that of model parameters from prior information. Based on the gradient of the objective function, a proposal distribution and an acceptance probability for MCMC samples are proposed. The proposed MCMC simulation is applied to several layered half-space examples. It is demonstrated that the proposed MCMC simulation for probabilistic FWI can estimate probabilistic material properties such as the shear-wave velocities of a layered half-space.

• Journal of information and communication convergence engineering
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• v.20 no.2
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• pp.79-89
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• 2022

To compute the mean and variance of component-based reliability software, we focused on path-based reliability analysis. System reliability depends on the transition probabilities of components within a system and reliability of the individual components as basic input parameters. The uncertainty in these parameters is estimated from the test data of the corresponding components and arises from the software architecture, failure behaviors, software growth models etc. Typically, researchers perform Monte Carlo simulations to study uncertainty. Thus, we considered a Markov chain Monte Carlo (MCMC) simulation to calculate uncertainty, as it generates random samples through sequential methods. The MCMC approach determines the input parameters from the probability distribution, and then calculates the average approximate expectations for a reliability estimation. The comparison of different techniques for uncertainty analysis helps in selecting the most suitable technique based on data requirements and reliability measures related to the number of components.

• The Korean Journal of Applied Statistics
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• v.27 no.4
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• pp.589-603
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• 2014

When consecutive data follows different distributions(depending on the time interval) change-point detection infers where the changes occur first and then finds further inferences for each sub-interval. In this paper, we investigate the Bayesian detection of multiple change points. Utilizing the reversible jump MCMC, we can explore parameter spaces with unknown dimensions. In particular, we consider a model where the signal is a piecewise linear function. For the Bayesian inference, we propose a new Bayesian structure and build our own MCMC algorithm. Through the simulation study and the real data analysis, we verified the performance of our method.

• 한국지구물리탐사학회:학술대회논문집
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• 2003.11a
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• pp.340-343
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• 2003

This study presents a practical procedure for the Bayesian inversion of geophysical data by Markov chain Monte Carlo (MCMC) sampling and geostatistics. We have applied geostatistical techniques for the acquisition of prior model information, and then the MCMC method was adopted to infer the characteristics of the marginal distributions of model parameters. For the Bayesian inversion of dipole-dipole array resistivity data, we have used the indicator kriging and simulation techniques to generate cumulative density functions from Schlumberger array resistivity data and well logging data, and obtained prior information by cokriging and simulations from covariogram models. The indicator approach makes it possible to incorporate non-parametric information into the probabilistic density function. We have also adopted the MCMC approach, based on Gibbs sampling, to examine the characteristics of a posteriori probability density function and the marginal distribution of each parameter. This approach provides an effective way to treat Bayesian inversion of geophysical data and reduce the non-uniqueness by incorporating various prior information.

• Structural Engineering and Mechanics
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• v.63 no.1
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• pp.47-53
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• 2017

The fundamental goal of this study is to minimize the uncertainty of the median fragility curve and to assess the structural vulnerability under earthquake excitation. Bayesian Inference with Markov Chain Monte Carlo (MCMC) simulation has been presented for efficient collapse response assessment of the independent intake water tower. The intake tower is significantly used as a diversion type of the hydropower station for maintaining power plant, reservoir and spillway tunnel. Therefore, the seismic fragility assessment of the intake tower is a pivotal component for estimating total system risk of the reservoir. In this investigation, an asymmetrical independent slender reinforced concrete structure is considered. The Bayesian Inference method provides the flexibility to integrate the prior information of collapse response data with the numerical analysis results. The preliminary information of risk data can be obtained from various sources like experiments, existing studies, and simplified linear dynamic analysis or nonlinear static analysis. The conventional lognormal model is used for plotting the fragility curve using the data from time history simulation and nonlinear static pushover analysis respectively. The Bayesian Inference approach is applied for integrating the data from both analyses with the help of MCMC simulation. The method achieves meaningful improvement of uncertainty associated with the fragility curve, and provides significant statistical and computational efficiency.

• Geophysics and Geophysical Exploration
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• v.5 no.4
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• pp.262-271
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• 2002

This study presents a practical procedure for the Bayesian inversion of geophysical data. We have applied geostatistical techniques for the acquisition of prior model information, then the Markov Chain Monte Carlo (MCMC) method was adopted to infer the characteristics of the marginal distributions of model parameters. For the Bayesian inversion of dipole-dipole array resistivity data, we have used the indicator kriging and simulation techniques to generate cumulative density functions from Schlumberger array resistivity data and well logging data, and obtained prior information by cokriging and simulations from covariogram models. The indicator approach makes it possible to incorporate non-parametric information into the probabilistic density function. We have also adopted the MCMC approach, based on Gibbs sampling, to examine the characteristics of a posteriori probability density function and the marginal distribution of each parameter.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.41 no.9
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• pp.1060-1068
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• 2016

The range-free localization using connectivity information has problems of mobile tracking. This paper proposes two Bayesian filter-based mobile tracking algorithms considering a propagation scenario. Kalman and Markov Chain Monte Carlo (MCMC) particle filters are applied according to linearity of two measurement models. Measurement models of the Kalman and MCMC particle filter-based algorithms respectively are defined as connectivity between mobiles, information fusion of connectivity information and received signal strength (RSS) from neighbors within one-hop. To perform the accurate simulation, we consider a real indoor map of shopping mall and degree of radio irregularity (DOI) model. According to obstacles between mobiles, we assume two types of DOIs. We show the superiority of the proposed algorithm over existing range-free algorithms through MATLAB simulations.

• Management Science and Financial Engineering
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• v.19 no.2
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• pp.49-53
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• 2013

A Markov-chain Monte Carlo sampling algorithm samples a new point around the latest sample due to the Markov property, which prevents it from sampling from multi-modal distributions since the corresponding chain often fails to search entire support of the target distribution. In this paper, to overcome this problem, mode switching scheme is applied to the conventional MCMC algorithms. The algorithm separates the reducible Markov chain into several mutually exclusive classes and use mode switching scheme to increase mixing rate. Simulation results are given to illustrate the algorithm with promising results.

• Proceedings of the Korea Water Resources Association Conference
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• 2021.06a
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• pp.127-127
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• 2021

In order to estimate parameter uncertainty of hydrological models, the consideration of the likelihood functions which provide reliable parameters of model is necessary. In this study, the Bayesian Markov Chain Monte Carlo (MCMC) method with informal likelihood functions is used to analyze the uncertainty of parameters of the SURR model for estimating the hourly streamflow of Gunnam station of Imjin basin, Korea. Three events were used to calibrate and one event was used to validate the posterior distributions of parameters. Moreover, the performance of four informal likelihood functions (Nash-Sutcliffe efficiency, Normalized absolute error, Index of agreement, and Chiew-McMahon efficiency) on uncertainty of parameter is assessed. The indicators used to assess the uncertainty of the streamflow simulation were P-factor (percentage of observed streamflow included in the uncertainty interval) and R-factor (the average width of the uncertainty interval). The results showed that the sensitivities of parameters strongly depend on the likelihood functions and vary for different likelihood functions. The uncertainty bounds illustrated the slight differences from various likelihood functions. This study confirms the importance of the likelihood function selection in the application of Bayesian MCMC to the uncertainty assessment of the SURR model.

• Smart Structures and Systems
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• v.15 no.3
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• pp.735-749
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• 2015

The major difficulty of using Bayesian probabilistic inference for system identification is to obtain the posterior probability density of parameters conditioned by the measured response. The posterior density of structural parameters indicates how plausible each model is when considering the uncertainty of prediction errors. The Markov chain Monte Carlo (MCMC) method is a widespread medium for posterior inference but its convergence is often slow. The differential evolution adaptive Metropolis-Hasting (DREAM) algorithm boasts a population-based mechanism, which nms multiple different Markov chains simultaneously, and a global optimum exploration ability. This paper proposes an improved differential evolution adaptive Metropolis-Hasting algorithm (IDREAM) strategy to estimate the posterior density of structural parameters. The main benefit of IDREAM is its efficient MCMC simulation through its use of the adaptive Metropolis (AM) method with a mutation strategy for ensuring quick convergence and robust solutions. Its effectiveness was demonstrated in simulations on identifying the structural parameters with limited output data and noise polluted measurements.