• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.1129-1140
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• 2005

A nonparametric Bayesian method for calculating posterior probabilities of the multiple comparison problem on the parameters of several Geometric populations is presented. Bayesian multiple comparisons under two different prior/ likelihood combinations was studied by Gopalan and Berry(1998) using Dirichlet process priors. In this paper, we followed the same approach to calculate posterior probabilities for various hypotheses in a statistical experiment with a partition on the parameter space induced by equality and inequality relationships on the parameters of several geometric populations. This also leads to a simple method for obtaining pairwise comparisons of probability of successes. Gibbs sampling technique was used to evaluate the posterior probabilities of all possible hypotheses that are analytically intractable. A numerical example is given to illustrate the procedure.

• Communications for Statistical Applications and Methods
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• v.21 no.2
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• pp.193-200
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• 2014

It was recognized by some researchers that the disturbance variance in a censored regression model is frequently underestimated by the maximum likelihood method. This underestimation has implications for the estimation of marginal effects and asymptotic standard errors. For instance, the actual coverage probability of the confidence interval based on a maximum likelihood estimate can be significantly smaller than the nominal confidence level; consequently, a Bayesian estimation is considered to overcome this difficulty. The behaviors of the maximum likelihood and Bayesian estimators of disturbance variance are examined in a fixed effects panel regression model with a limited dependent variable, which is known to have the incidental parameter problem. Behavior under random effect assumption is also investigated.

• Journal of Applied Reliability
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• v.17 no.3
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• pp.188-196
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• 2017

Purpose: The purpose of this research is to determine optimal replacement age using non-informative prior information and Bayesian method. Methods: We propose a novel approach using Bayesian method to determine the optimal replacement age in block replacement policy by defining the prior probability with data on failure time and repair time. The Marcov Chain Monte Carlo simulation is used to investigate the asymptotic distribution of posterior parameters. Results: An optimal replacement age of block replacement policy is determined which minimizes cost and nonoperating time when no information on prior distribution of parameters is given. Conclusion: We find the posterior distribution of parameters when lack of information on prior distribution, so that the optimal replacement age which minimizes the total cost and maximizes the total values is determined.

• Communications for Statistical Applications and Methods
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• v.14 no.2
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• pp.431-442
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• 2007

In this paper, we develop the noninformative priors when the parameter of interest is the difference between quantiles of two exponential distributions. We want to develop the first and second order probability matching priors. But we prove that the second order probability matching prior does not exist. It turns out that Jeffreys' prior does not satisfy the first order matching criterion. The Bayesian credible intervals based on the first order probability matching prior meet the frequentist target coverage probabilities much better than the frequentist intervals of Jeffreys' prior. Some simulation and real example will be given.

• The Korean Journal of Applied Statistics
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• v.33 no.1
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• pp.25-46
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• 2020

This paper presents ordinal probit semiparametric regression models using Bayesian Spectral Analysis Regression (BSAR) method. Ordinal probit regression is a way of modeling ordinal responses - usually more than two categories - by connecting the probability of falling into each category explained by a combination of available covariates using a probit (an inverse function of normal cumulative distribution function) link. The Bayesian probit model facilitates posterior sampling by bringing a latent variable following normal distribution, therefore, the responses are categorized by the cut-off points according to values of latent variables. In this paper, we extend the latent variable approach to a semiparametric model for the Bayesian ordinal probit regression with nonparametric functions using a spectral representation of Gaussian processes based BSAR method. The latent variable is decomposed into a parametric component and a nonparametric component with or without a shape constraint for modeling ordinal responses and predicting outcomes more flexibly. We illustrate the proposed methods with simulation studies in comparison with existing methods and real data analysis applied to a Korean National Health and Nutrition Examination Survey (KNHANES) 2016 for investigating nonparametric relationship between smoking behavior and coffee intake.

• Journal of Korean Society for Quality Management
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• v.44 no.2
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• pp.221-244
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• 2016

Purpose: This research reviews the papers, published in the Journal of the Korean Society for Quality Control (KSQC) and the Journal of the Korean Society for Quality Management (KSQM) since 1965, in the area of statistical methods. The literature review is performed in the four fields of the statistical methods and we categorize the published articles into the several sub-areas in each field. Methods: The reviewed articles are classified into the four main categories: probability model and estimation, Bayesian analysis and non-parametric analysis, regression and time series analysis, and application of data analysis. We examine the contents and relationships of the published articles of the several sub-areas in each category. Results: We summarize the reviewed papers in the chronological road-maps for each sub-area, and outline the relations of the connected papers. Some comments on the contents and the contributions of the reviewed papers are also provided in this paper. Conclusion: Various issues are employed and published on the research of the application statistical methods for past 50 years, and many worthy works are achieved in the theory and application areas of statistical methods for improving quality in the manufacturing and service industries. The future direction of the research in the statistical quality management methods also can be explored by the contents of this research.

• Journal of the Korean Statistical Society
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• v.27 no.4
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• pp.407-420
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• 1998

This paper is concerned with selecting covariates to be included in building linear random effects models designed to analyze clustered response normal data. It is based on a Bayesian approach, intended to propose and develop a procedure that uses probabilistic considerations for selecting premising subsets of covariates. The approach reformulates the linear random effects model in a hierarchical normal and point mass mixture model by introducing a set of latent variables that will be used to identify subset choices. The hierarchical model is flexible to easily accommodate sign constraints in the number of regression coefficients. Utilizing Gibbs sampler, the appropriate posterior probability of each subset of covariates is obtained. Thus, In this procedure, the most promising subset of covariates can be identified as that with highest posterior probability. The procedure is illustrated through a simulation study.

• Communications for Statistical Applications and Methods
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• v.15 no.3
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• pp.429-440
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• 2008

In this paper, we develop the noninformative priors when the parameter of interest is the common coefficient of variation in two inverse Gaussian distributions. We want to develop the first and second order probability matching priors. But we prove that the second order probability matching prior does not exist. It turns out that the one-at-a-time and two group reference priors satisfy the first order matching criterion but Jeffreys' prior does not. The Bayesian credible intervals based on the one-at-a-time reference prior meet the frequentist target coverage probabilities much better than that of Jeffreys' prior. Some simulations are given.

• The Korean Journal of Applied Statistics
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• v.24 no.5
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• pp.951-961
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• 2011

In this paper, we propose a Bayesian inference using the Markov Chain Monte Carlo(MCMC) method for the zero inflated negative binomial(ZINB) regression model. The proposed model allows the regression model for zero inflation probability as well as the regression model for the mean of the dependent variable. This extends the work of Jang et al. (2010) to the fully defiend ZINB regression model. In addition, we apply the proposed method to a real data example, and compare the efficiency with the zero inflated Poisson model using the DIC. Since the DIC of the ZINB is smaller than that of the ZIP, the ZINB model shows superior performance over the ZIP model in zero inflated count data with overdispersion.

• Economic and Environmental Geology
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• v.38 no.6 s.175
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• pp.663-673
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• 2005

This study investigates the relationship between the geochemical maps and the gold-silver deposit locations. Geochemical maps of 21 elements, which are published by KIGAM, locations of gold-silver deposits, and 1:1,000,000 scale geological map of Korea are utilized far this investigation. Pixel size of the basic geochemical maps is 250m and these data are resampled in 1km spacing for the statistical analyses. Relationship between the mine location and the geochemical data are investigated using bayesian statistics and decision tree algorithms. For the bayesian statistics, each geochemical maps are reclassified by percentile divisions which divides the data by 5, 25, 50, 75, 95, and $100\%$ data groups. Number of mine locations in these divisions are counted and the probabilities are calculated. Posterior probabilities of each pixel are calculated using the probability of 21 geochemical maps and the geological map. A prediction map of the mining locations is made by plotting the posterior probability. The input parameters for the decision tree construction are 21 geochemical elements and lithology, and the output parameters are 5 types of mines (Ag/Au, Cu, Fe, Pb/Zn, W) and absence of the mine. The locations for the absence of the mine are selected by resampling the overall area by 1 km spacing and eliminating my resampled points, which is in 750m distance from mine locations. A prediction map of each mine area is produced by applying the decision tree to every pixels. The prediction by Bayesian method is slightly better than the decision tree. However both prediction maps show reasonable match with the input mine locations. We interpret that such match indicate the rules produced by both methods are reasonable and therefore the geochemical data has strong relations with the mine locations. This implies that the geochemical rules could be used as background values oi mine locations, therefore could be used for evaluation of mine contamination. Bayesian statistics indicated that the probability of Au/Ag deposit increases as CaO, Cu, MgO, MnO, Pb and Li increases, and Zr decreases.