• Journal of Korean Institute of Industrial Engineers
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• v.42 no.4
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• pp.256-262
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• 2016

The Weibull is widely used in reliability analysis, and several studies have attempted to improve estimation of the distribution's parameters. least squares estimation (LSE) or Maximum likelihood estimation (MLE) are often used to estimate distribution parameters. However, it has been proven that Bayesian methods are more suitable for small sample sizes than LSE and MLE. In this work, the Weibull parameter estimation accuracy of LSE, MLE, and Bayesian method are compared for sample sets with 3 to 30 data points. The Bayesian method was most accurate for sample sizes under 25, and the accuracy of the Bayesian method was similar to LSE and MLE as the sample size increased.

• Korean Management Science Review
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• v.34 no.2
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• pp.15-33
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• 2017

This paper considers a Bayesian Network analysis for understanding the heterogeneous cross-category effects of different promotion activities and developing an efficient overall promotion strategy for a large retail store. More specifically we differentiate price reduction promotion and floor promotion and study their heterogeneous effect on consumer purchase behavior under a market basket setting. We then utilize Bayesian networks in identifying complex association structure in market basket dataset by analyzing the effects of different promotional activities and also include the effects of time, family income and size. We find from our Bayesian network analysis that the dominant cross-category promotion effect of price promotion is the indirect effect whereas the dominant cross-category promotion effect of floor promotion is the direct effect. Also, among the demographic variables we find that family size of the household is linked with more product categories compared to income and see that there are differences in the extent of the effects by product category. Finally, we also show the existence of products acting as a network hub and how they can be utilized by retailers faced with a limited marketing budget and suggest a more efficient promotion strategy.

• Journal of Applied Reliability
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• v.17 no.3
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• pp.213-223
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• 2017

Purpose: The purpose of this study is to arrange the life data analysis literatures based on the Bayesian method quantitatively and provide it as tables. Methods: The Bayesian method produces a more accurate estimates of other traditional methods in a small sample size, and it requires specific algorithm and prior information. Based on these three characteristics of the Bayesian method, the criteria for classifying the literature were taken into account. Results: In many studies, there are comparisons of estimation methods for the Bayesian method and maximum likelihood estimation (MLE), and sample size was greater than 10 and not more than 25. In probability distributions, a variety of distributions were found in addition to the distributions of Weibull commonly used in life data analysis, and MCMC and Lindley's Approximation were used evenly. Finally, Gamma, Uniform, Jeffrey and extension of Jeffrey distributions were evenly used as prior information. Conclusion: To verify the characteristics of the Bayesian method which are more superior to other methods in a smaller sample size, studies in less than 10 samples should be carried out. Also, comparative study is required by various distributions, thereby providing guidelines necessary.

• Journal of the Korean Statistical Society
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• v.23 no.2
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• pp.463-482
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• 1994

In Bayesian analysis of randomized response models, the likelihood function does not combine tractably with typical priors for the parameters of interest, causing computational difficulties in posterior analysis of the parameters of interest. In this article, the difficulties are solved by introducing appropriate latent variables to the model and using the Gibbs sampling algorithm.

• Smart Structures and Systems
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• v.15 no.2
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• pp.395-408
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• 2015

This study aims to propose a Bayesian approach to consider changes in temperature and vehicle weight as environmental and operational factors for vibration-based long-term bridge health monitoring. The Bayesian approach consists of three steps: step 1 is to identify damage-sensitive features from coefficients of the auto-regressive model utilizing bridge accelerations; step 2 is to perform a regression analysis of the damage-sensitive features to consider environmental and operational changes by means of the Bayesian regression; and step 3 is to make a decision on the bridge health condition based on residuals, differences between the observed and predicted damage-sensitive features, utilizing 95% confidence interval and the Bayesian hypothesis testing. Feasibility of the proposed approach is examined utilizing monitoring data on an in-service bridge recorded over a one-year period. Observations through the study demonstrated that the Bayesian regression considering environmental and operational changes led to more accurate results than that without considering environmental and operational changes. The Bayesian hypothesis testing utilizing data from the healthy bridge, the damage probability of the bridge was judged as no damage.

• Proceedings of the Korea Water Resources Association Conference
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• 2008.05a
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• pp.1125-1128
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• 2008

본 연구에서는 Bayesian MCMC 방법과 2차 근사식을 이용한 최우추정(Maximum Likelihood Estimation, MLE)방법 방법을 이용하여 낙동강 유역의 본류지점인 낙동, 왜관, 고령교, 진동지점에 대한 점 빈도분석을 수행하고 그 결과로써 불확실성을 포함한 빈도곡선을 작성하였다. 통계적 실험을 통한 두 가지 추정방법의 분석을 위하여 먼저 자료의 길이가 100인 8개의 합성 유량자료 셋을 생성하여 비교 연구를 수행하였으며, 이를 자료길이 36인 실측 유량자료의 추정결과와 비교하였다. Bayesian MCMC 방법에 의한 평균값과 2차 근사식을 이용한 취우추정방법에 의한 모드에서의 2모수 Weibull 분포의 모수 추정값은 비슷한 결과를 보였으나, 불확실성을 나타내는 하한값과 상한값의 차이는 Bayesian MCMC 방법이 2차 근사식을 이용한 취우추정방법보다 불확실성을 감소시켜 나타내는 것을 알 수 있었다. 또한 실측 유량자료를 이용한 결과, 2차 근사식을 이용한 최우추정방법의 경우 자료의 길이가 감소됨에 따라 불확실성의 범위가 합성 유량자료를 사용한 경우에 비해 상대적으로 증가되지만, Bayesian MCMC 방법의 경우에는 자료의 길이에 대한 영향이 거의 없다는 결론을 얻을 수 있었다. 그러므로 저수량 빈도분석을 수행하기 위해 충분한 자료를 확보할 수 없는 국내의 상황을 감안할 때, 위와 같은 결론으로부터 Bayesian MCMC 방법이 불확실성을 표현하는데 있어서 2차 근사식을 이용한 최우추정방법에 비해 합리적일 수 있다는 결론을 얻을 수 있었다.

• Smart Structures and Systems
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• v.17 no.3
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• pp.445-470
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• 2016

In this study, the Bayesian probabilistic framework is investigated for modal identification and modal identifiability based on the field measurements provided in the structural health monitoring benchmark problem of an instrumented cable-stayed bridge named Ting Kau Bridge (TKB). The comprehensive structural health monitoring system on the cable-stayed TKB has been operated for more than ten years and it is recognized as one of the best test-beds with readily available field measurements. The benchmark problem of the cable-stayed bridge is established to stimulate investigations on modal identifiability and the present paper addresses this benchmark problem from the Bayesian prospective. In contrast to deterministic approaches, an appealing feature of the Bayesian approach is that not only the optimal values of the modal parameters can be obtained but also the associated estimation uncertainty can be quantified in the form of probability distribution. The uncertainty quantification provides necessary information to evaluate the reliability of parametric identification results as well as modal identifiability. Herein, the Bayesian spectral density approach is conducted for output-only modal identification and the Bayesian model class selection approach is used to evaluate the significance of different modes in modal identification. Detailed analysis on the modal identification and modal identifiability based on the measurements of the bridge will be presented. Moreover, the advantages and potentials of Bayesian probabilistic framework on structural health monitoring will be discussed.

• The Korean Journal of Applied Statistics
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• v.27 no.6
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• pp.1029-1038
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• 2014

Bayesian experimental design is a useful concept in applied statistics for the design of efficient experiments especially if prior knowledge in the experiment is available. However, a theoretical or numerical approach is not simple to implement. We review the concept of a Bayesian experiment approach for linear and nonlinear statistical models. We investigate relationships between prior knowledge and optimal design to identify Bayesian experimental design process characteristics. A balanced design is important if we do not have prior knowledge; however, prior knowledge is important in design and expert opinions should reflect an efficient analysis. Care should be taken if we set a small sample size with a vague improper prior since both Bayesian design and non-Bayesian design provide incorrect solutions.

• Journal of Korea Water Resources Association
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• v.47 no.10
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• pp.853-865
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• 2014

Hydrologic dam risk analysis depends on complex hydrologic analyses in that probabilistic relationship need to be established to quantify various uncertainties associated modeling process and inputs. However, the systematic approaches to uncertainty analysis for hydrologic risk analysis have not been addressed yet. In this paper, two major innovations are introduced to address this situation. The first is the use of a Hierarchical Bayesian model based regional frequency analysis to better convey uncertainties associated with the parameters of probability density function to the dam risk analysis. The second is the use of Bayesian model coupled HEC-1 rainfall-runoff model to estimate posterior distributions of the model parameters. A reservoir routing analysis with the existing operation rule was performed to convert the inflow scenarios into water surface level scenarios. Performance functions for dam risk model was finally employed to estimate hydrologic dam risk analysis. An application to the Dam in South Korea illustrates how the proposed approach can lead to potentially reliable estimates of dam safety, and an assessment of their sensitivity to the initial water surface level.

• Earthquakes and Structures
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• v.12 no.6
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• pp.653-663
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• 2017

A seismic margin assessment evaluates how much margin exists for the system under beyond design basis earthquake events. Specifically, the seismic margin for the entire system is evaluated by utilizing a systems analysis based on the sub-system and component seismic fragility data. Each seismic fragility curve is obtained by using empirical, experimental, and/or numerical simulation data. The systems analysis is generally performed by employing a fault tree analysis. However, the current practice has clear limitations in that it cannot deal with the uncertainties of basic components and accommodate the newly observed data. Therefore, in this paper, we present a Bayesian-based seismic margin assessment that is conducted using seismic fragility data and fault tree analysis including Bayesian inference. This proposed approach is first applied to the pooltype nuclear research reactor system for the quantitative evaluation of the seismic margin. The results show that the applied approach can allow updating by considering the newly available data/information at any level of the fault tree, and can identify critical scenarios modified due to new information. Also, given the seismic hazard information, this approach is further extended to the real-time risk evaluation. Thus, the proposed approach can finally be expected to solve the fundamental restrictions of the current method.