• Journal of the Korean Statistical Society
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• v.30 no.2
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• pp.179-192
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• 2001

When a statistical model has a hierarchical structure such as multilayer perceptrons in neural networks or Gaussian mixture density representation, the model includes distribution with unidentifiable parameters when the structure becomes redundant. Since the exact structure is unknown, we need to carry out statistical estimation or learning of parameters in such a model. From the geometrical point of view, distributions specified by unidentifiable parameters become a singular point in the parameter space. The problem has been remarked in many statistical models, and strange behaviors of the likelihood ratio statistics, when the null hypothesis is at a singular point, have been analyzed so far. The present paper studies asymptotic behaviors of the maximum likelihood estimator and the Bayesian predictive estimator, by using a simple cone model, and show that they are completely different from regular statistical models where the Cramer-Rao paradigm holds. At singularities, the Fisher information metric degenerates, implying that the cramer-Rao paradigm does no more hold, and that he classical model selection theory such as AIC and MDL cannot be applied. This paper is a first step to establish a new theory for analyzing the accuracy of estimation or learning at around singularities.

• Journal of Korea Water Resources Association
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• v.48 no.1
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• pp.37-44
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• 2015

A Bayesian nonstationary probability rainfall estimation model using the Grid method is developed. A hierarchical Bayesian framework is consisted with prior and hyper-prior distributions associated with parameters of the Gumbel distribution which is selected for rainfall extreme data. In this study, the Grid method is adopted instead of the Matropolis Hastings algorithm for random number generation since it has advantage that it can provide a thorough sampling of parameter space. This method is good for situations where the best-fit parameter values are not easily inferred a priori, and where there is a high probability of false minima. The developed model was applied to estimated target year probability rainfall using hourly rainfall data of Seoul station from 1973 to 2012. Results demonstrated that the target year estimate using nonstationary assumption is about 5~8% larger than the estimate using stationary assumption.

• Journal of the Korean Data and Information Science Society
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• v.18 no.4
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• pp.1179-1189
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• 2007

In this paper, we estimate the proportion of individuals having health insurance in a given year for several small domains cross-classified by age, sex and other demographic characteristics using the data provided by the National Center for Health Statistics(NCHS). We employ Bayesian as well as frequentist methodology to obtain small domain estimates and the associated measures of precision. One of the new features of our study is that we utilize the survey weights along with the model to derive the small domain estimates.

• 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.

• The Korean Journal of Applied Statistics
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• v.28 no.2
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• pp.137-149
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• 2015

Flood planning needs to recognize trends for extreme precipitation events. Especially, the r-year return level is a common measure for extreme events. In this paper, we present a nonstationary temporal model for precipitation return levels using a hierarchical Bayesian modeling. For intensity, we model annual maximum daily precipitation measured in Korea with a generalized extreme value (GEV). The temporal dependence among the return levels is incorporated to the model for GEV model parameters and a linear model with autoregressive error terms. We apply the proposed model to precipitation data collected from various stations in Korea from 1973 to 2011.

• Communications for Statistical Applications and Methods
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• v.19 no.3
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• pp.495-500
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• 2012

We consider a Bayesian test of independence in a two-way contingency table that has some zero cells. To do this, we take a three-stage hierarchical Bayesian model under each hypothesis. For prior, we use Dirichlet density to model the marginal cell and each cell probabilities. Our method does not require complicated computation such as a Metropolis-Hastings algorithm to draw samples from each posterior density of parameters. We draw samples using a Gibbs sampler with a grid method. For complicated posterior formulas, we apply the Monte-Carlo integration and the sampling important resampling algorithm. We compare the values of the Bayes factor with the results of a chi-square test and the likelihood ratio test.

• 한국데이터정보과학회:학술대회논문집
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• 2005.04a
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• pp.83-126
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• 2005

Single-index models have found applications in econometrics and biometrics, where multidimensional regression models are often encountered. Here we propose a nonparametric estimation approach that combines wavelet methods for non-equispaced designs with Bayesian models. We consider a wavelet series expansion of the unknown regression function and set prior distributions for the wavelet coefficients and the other model parameters. To ensure model identifiability, the direction parameter is represented via its polar coordinates. We employ ad hoc hierarchical mixture priors that perform shrinkage on wavelet coefficients and use Markov chain Monte Carlo methods for a posteriori inference. We investigate an independence-type Metropolis-Hastings algorithm to produce samples for the direction parameter. Our method leads to simultaneous estimates of the link function and of the index parameters. We present results on both simulated and real data, where we look at comparisons with other methods.

• Journal of Korea Water Resources Association
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• v.54 no.10
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• pp.747-757
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• 2021

Quantification of extreme rainfall is very important in establishing a flood protection plan, and a general measure of extreme rainfall is expressed as an T-year return level. In this study, a method was proposed for quantifying spatial distribution and uncertainty of daily rainfall depths with various return periods using a hierarchical Bayesian model combined with climate and geographical information, and was applied to the Seoul-Incheon-Gyeonggi region. The annual maximum daily rainfall depth of six automated synoptic observing system weather stations of the Korea Meteorological Administration in the study area was fitted to the generalized extreme value distribution. The applicability and reliability of the proposed method were investigated by comparing daily rainfall quantiles for various return levels derived from the at-site frequency analysis and the regional frequency analysis based on the index flood method. The uncertainty of the regional frequency analysis based on the index flood method was found to be the greatest at all stations and all return levels, and it was confirmed that the reliability of the regional frequency analysis based on the hierarchical Bayesian model was the highest. The proposed method can be used to generate the rainfall quantile maps for various return levels in the Seoul-Incheon-Gyeonggi region and other regions with similar spatial sizes.

• The Korean Journal of Applied Statistics
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• v.24 no.4
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• pp.609-622
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• 2011

The pattern of methylation draws significant attention from cancer researchers because it is believed that DNA methylation and gene expression have a causal relationship. As the interest in the role of methylation patterns in cancer studies (especially drug resistant cancers) increases, many studies have been done investigating the association between gene expression and methylation. However, a model-based approach is still in urgent need. We developed a finite mixture model in the Bayesian framework to find a possible relationship between gene expression and methylation. For inference, we employ Expectation-Maximization(EM) algorithm to deal with latent (unobserved) variable, producing estimates of parameters in the model. Then we validated our model through simulation study and then applied the method to real data: wild type and hydroxytamoxifen(OHT) resistant MCF7 breast cancer cell lines.

• Proceedings of the Korea Water Resources Association Conference
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• 2018.05a
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• pp.168-168
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• 2018

최근 기후변화로 인하여 전 세계적으로 과거 강우사상에서 확인되지 않는 극치사상이 빈번하게 관측되고 있으며 이에 따른 피해도 증가하고 있다. 미래의 기상학적 변동성 및 기후변화 영향은 지구순환모형 (General Circulation Models, GCM)을 통해 구체화되며 가장 일반적인 기후변화 전망자료로서 활용된다. 그러나 산정된 기후변화 시나리오마다 서로 그 특성에 차이가 있으며 이러한 이유로 다양한 원인으로 인해 큰 변동성을 가지는 미래 극치강우를 하나의 시나리오로 분석하기에는 무리가 있다. 또한 다양한 시나리오를 통해 분석한 결과값이 상이하며 이러한 시나리오별 산정 결과의 차이는 사용자에게 혼란을 야기할 수 있어 이를 하나의 결과로 나타낼 필요성이 있으나 정량적인 대푯값을 얻기 위해 특정 시나리오를 선택하는 것은 신뢰성에 문제가 있다. 본 연구에서는 시나리오들을 정량적 지표에 의거하여 혼합된 하나의 시나리오로 표출하고자 하였다. CORDEX-RCMs 시나리오 중 HadGEM3-RA, RegCM, SNU_WRF 및 GRIMs를 입력 자료로 하여 다중모형앙상블(Multi-Model Ensemble, MME)을 통해 낙동강 유역의 극치강우에 대한 하나의 최적 기후변화 시나리오를 도출하고자 하였으며 계층적 베이지안 (Hierarchical Bayesian Model, HBM) 기법을 통하여 기후변화 시나리오에 내제된 불확실성에 대한 정량적인 해석을 수행하였다.