• Communications for Statistical Applications and Methods
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• v.6 no.1
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• pp.181-191
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• 1999

We consider Bayesian models allow multiple grouping of parameters for the normal means estimation problem. In particular, we consider a typical Bayesian hierarchical approach based on thepartial exchangeability where the components within a subgroup are exchangeable, but the different subgroups are not. We discuss implementation of such Bayesian procedures via Gibbs sampling. We illustrate the proposed methods with numerical examples.

• Communications for Statistical Applications and Methods
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• v.2 no.2
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• pp.43-51
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• 1995

For the stress-strengh function, hierarchical Bayes estimations considered under squared error loss and entropy loss. In particular, the desired marginal postrior densities ate obtained via Gibbs sampler, an iterative Monte Carlo method, and Normal approximation (by Delta method). A simulation is presented.

• Journal of the Korean Statistical Society
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• v.31 no.1
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• pp.45-61
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• 2002

We consider the problem of estimating binomial proportions in the presence of nonignorable nonresponse using the Bayesian selection approach. Inference is sampling based and Markov chain Monte Carlo (MCMC) methods are used to perform the computations. We apply our method to study doctor visits data from the Korean National Family Income and Expenditure Survey (NFIES). The ignorable and nonignorable models are compared to Stasny's method (1991) by measuring the variability from the Metropolis-Hastings (MH) sampler. The results show that both models work very well.

• Journal of the Korean Data and Information Science Society
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• v.26 no.3
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• pp.749-754
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• 2015

This article presents Bayesian approach to regression splines with knots on a grid of equally spaced sample quantiles of the independent variables under functional measurement error model.We consider small area model by using penalized splines of non-linear pattern. Specifically, in a basis functions of the regression spline, we use radial basis functions. To fit the model and estimate parameters we suggest a hierarchical Bayesian framework using Markov Chain Monte Carlo methodology. Furthermore, we illustrate the method in an application data. We check the convergence by a potential scale reduction factor and we use the posterior predictive p-value and the mean logarithmic conditional predictive ordinate to compar models.

• Management Science and Financial Engineering
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• v.12 no.2
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• pp.19-35
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• 2006

We use the hierarchical Bayesian approach to describe the transition probabilities of a binary nonhomogeneous Markov chain. The Markov chain is used for describing the transition behavior of emotionally disturbed children in a treatment program. The effects of covariates on transition probabilities are assessed using a logit link function. To describe the time evolution of transition probabilities, we consider two modeling strategies. The first strategy is based on the concept of exchangeabiligy, whereas the second one is based on a first order Markov property. The deviance information criterion (DIC) measure is used to compare models with two different time dependent structures. The inferences are made using the Markov chain Monte Carlo technique. The developed methodology is applied to some real data.

• The Korean Journal of Applied Statistics
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• v.27 no.2
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• pp.263-275
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• 2014

The present study used a hierarchical Bayesian approach was used to develop a mixed effect model to describe the transitional behavior of subjects in time nonhomogeneous Markov chains. The posterior distributions of model parameters were not in analytically tractable forms; subsequently, a Gibbs sampling method was used to draw samples from full conditional posterior distributions. The proposed model was implemented with real data.

• Proceedings of the Korea Water Resources Association Conference
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• 2016.05a
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• pp.36-36
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• 2016

하천정비나 유역종합 치수계획 등 수자원계획을 수립하는 과정에 있어 하천의 설계홍수량 추정은 필수적이며, 하천의 수공구조물의 안전성과 수문학적 위험도를 산정하는데도 활용되고 있다. 그러나 매년 관측되는 강우량 자료에 비해 유출량 자료의 길이가 비교적 짧아 신뢰성 있는 홍수량자료의 구축이 어려운 실정이며, 미계측 유역에 위치한 중소규모 하천의 설계홍수량과 같은 수문학적 자료는 매우 제한적이다. 이러한 이유로 본 연구에서는 기 수립된 하천정비기본계획의 자료들을 활용하여 유역의 특성(면적, 경사, 고도)이 고려되는 새로운 홍수량 산정식을 개발하였으며, Bayesian GLM(generalized linear method) 기법을 활용하여 미계측 유역의 지역화를 통한 홍수량의 추정이 가능하도록 하였다. 또한 Hierarchical Bayesian 기법을 활용하여 개발된 공식에 활용되는 매개변수의 불확실성을 구간을 산정하였다. Bayesian 기법의 도입으로 산정되는 홍수량의 불확실성 구간을 정량적으로 제시할 수 있었으며, 제안된 연구 결과는 미계측 유역의 홍수량을 추정하는 도구로서 활용성이 높을 것으로 기대된다.

• Communications for Statistical Applications and Methods
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• v.25 no.2
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• pp.131-157
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• 2018

We propose a robust event date model to estimate the date of a target event by a combination of individual dates obtained from archaeological artifacts assumed to be contemporaneous. These dates are affected by errors of different types: laboratory and calibration curve errors, irreducible errors related to contaminations, and taphonomic disturbances, hence the possible presence of outliers. Modeling based on a hierarchical Bayesian statistical approach provides a simple way to automatically penalize outlying data without having to remove them from the dataset. Prior information on individual irreducible errors is introduced using a uniform shrinkage density with minimal assumptions about Bayesian parameters. We show that the event date model is more robust than models implemented in BCal or OxCal, although it generally yields less precise credibility intervals. The model is extended in the case of stratigraphic sequences that involve several events with temporal order constraints (relative dating), or with duration, hiatus constraints. Calculations are based on Markov chain Monte Carlo (MCMC) numerical techniques and can be performed using ChronoModel software which is freeware, open source and cross-platform. Features of the software are presented in Vibet et al. (ChronoModel v1.5 user's manual, 2016). We finally compare our prior on event dates implemented in the ChronoModel with the prior in BCal and OxCal which involves supplementary parameters defined as boundaries to phases or sequences.

• Proceedings of the Korea Water Resources Association Conference
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• 2015.05a
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• pp.466-466
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• 2015

지역빈도해석은 수문학에서 오랜 역사를 갖고 있으며, 수년에 걸쳐 수문학적 변량의 정량적 추정을 위해 다양한 접근방법들이 제안되어 왔다. 그러나 제안된 방법들의 가설설정 수준이 높기 때문에 실제 적용에 제약이 많고, 적용 시에도 예측에 대한 불확실성이 높은 문제점이 있다. 본 연구에서는 이러한 문제점을 개선하기 위한 방법으로 계층적 베이지안 모델을 이용한 지역빈도해석 모형을 제안하고자 한다. 본 모형은 2개의 계층적 구조로 구성된다. 첫번째 계층은 재현기간별 GEV 분포의 매개변수를 정규화하여 주변분포로 설정하고, Kriging 기법을 이용하여 지형학적, 기상학적 정보들과 극치강수량 효과를 적합시켜 공간적 이질성과 미계측 유역에 대한 효과적인 보간을 가능하게 한다. 두번째 계층은 지점의 특성을 나타내는 매개변수들간의 공분산을 Bayesian 모델에 연계하여 매개변수들의 공간적 변동성을 나타낸다. 2개 계층의 결합확률분포는 MCMC 기법을 이용하여 예측값에 대한 불확실성을 정량적으로 분석하게 된다. 본 모형을 통해 홍수량 추정 시 필요한 시간 단위 극치강수량의 공간적 분포를 효과적으로 추정할 수 있을 것으로 판단된다.

• The Korean Journal of Applied Statistics
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• v.22 no.2
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• pp.425-433
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• 2009

Spatial models suitable for describing the evolving random fields in climate and environmental systems have been developed by many researchers. In general, rainfall in South Korea is highly variable in intensity and amount across space. This study characterizes the monthly and regional variation of rainfall fields using the spatial modeling. The main objective of this research is spatial prediction with the Bayesian hierarchical modeling (kriging) in order to further our understanding of water resources over space. We use the Bayesian approach in order to estimate the parameters and produce more reliable prediction. The Bayesian kriging also provides a promising solution for analyzing and predicting rainfall data.