• 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.10 no.3
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• pp.981-996
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• 2003

Bayesian inference is considered for switching mean models with the ARMA errors. We use noninformative improper priors or uniform priors. The fractional Bayes factor of O'Hagan (1995) is used as the Bayesian tool for detecting the existence of a single change or multiple changes and the usual Bayes factor is used for identifying the orders of the ARMA error. Once the model is fully identified, the Gibbs sampler with the Metropolis-Hastings subchains is constructed to estimate parameters. Finally, we perform a simulation study to support theoretical results.

• Journal of the Korean Data and Information Science Society
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• v.7 no.2
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• pp.247-256
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• 1996

In this paper, we applied bayesian hierarchical model to analyze the field mice example introduced by Demster et al.(1981). For this example, we use Gibbs sampler method to provide the posterior mean and compared it with LSE(Least Square Estimator) and MLR(Maximum Likelihood estimator with Random effect) via the EM algorithm.

• Journal of the Korean Data and Information Science Society
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• v.12 no.1
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• pp.1-9
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• 2001

In this paper, the problem of information related to I binomial experiments, each having a distinct probability of success ${\theta}_i$, i = 1,2, $\cdots$, I, is considered. Instead of using a standard exchangeable prior for ${\theta}\;=\;({\theta}_1,\;{\theta}_2,\;{\cdots},\;{\theta}_I)$, we con-sider a partition of the experiments and take the ${\theta}_i$'s belonging to the same partition subset to be exchangeable and the ${\theta}_i$'s belonging to distinct subsets to be independent. And we perform Gibbs sampler approach for Bayesian inference on $\theta$ conditional on a partition. Also we illustrate the methodology with a real data.

• Journal of the Korean Statistical Society
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• v.26 no.4
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• pp.493-505
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• 1997

The analysis of binary data appears to many areas such as statistics, biometrics and econometrics. In many cases, data are often collected in which some observations are incomplete. Assume that the missing covariates are missing at random and the responses are completely observed. A method to Bayesian analysis of the binary regression model with incomplete data is presented. In particular, the desired marginal posterior moments of regression parameter are obtained using Meterpolis algorithm (Metropolis et al. 1953) within Gibbs sampler (Gelfand and Smith, 1990). Also, we compare logit model with probit model using Bayes factor which is approximated by importance sampling method. One example is presented.

• Communications for Statistical Applications and Methods
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• v.9 no.1
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• pp.155-166
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• 2002

Neural networks have been studied as a popular tool for classification and they are very flexible. Also, they are used for many applications of pattern classification and pattern recognition. This paper focuses on Bayesian approach to feed-forward neural networks with single hidden layer of units with logistic activation. In this model, we are interested in deciding the number of nodes of neural network model with p input units, one hidden layer with m hidden nodes and one output unit in Bayesian setup for fixed m. Here, we use the latent variable into the prior of the coefficient regression, and we introduce the 'sequential step' which is based on the idea of the data augmentation by Tanner and Wong(1787). The MCMC method(Gibbs sampler and Metropolish algorithm) can be used to overcome the complicated Bayesian computation. Finally, a proposed method is applied to a simulated data.

• Journal of the Korean Statistical Society
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• v.28 no.2
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• pp.167-182
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• 1999

This article is concerned with the selection of subsets of predictor variables to be included in building the binary response probit regression model. It is based on a Bayesian approach, intended to propose and develop a procedure that uses probabilistic considerations for selecting promising subsets. This procedure reformulates the probit regression setup in a hierarchical normal mixture model by introducing a set of hyperparameters that will be used to identify subset choices. The appropriate posterior probability of each subset of predictor variables is obtained through the Gibbs sampler, which samples indirectly from the multinomial posterior distribution on the set of possible subset choices. Thus, in this procedure, the most promising subset of predictors can be identified as the one with highest posterior probability. To highlight the merit of this procedure a couple of illustrative numerical examples are given.

• Communications for Statistical Applications and Methods
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• v.21 no.2
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• pp.147-160
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• 2014

In this paper, we introduce the exponentiated Weibull-geometric (EWG) distribution which generalizes two-parameter exponentiated Weibull (EW) distribution introduced by Mudholkar et al. (1995). This proposed distribution is obtained by compounding the exponentiated Weibull with geometric distribution. We derive its cumulative distribution function (CDF), hazard function and the density of the order statistics and calculate expressions for its moments and the moments of the order statistics. The hazard function of the EWG distribution can be decreasing, increasing or bathtub-shaped among others. Also, we give expressions for the Renyi and Shannon entropies. The maximum likelihood estimation is obtained by using EM-algorithm (Dempster et al., 1977; McLachlan and Krishnan, 1997). We can obtain the Bayesian estimation by using Gibbs sampler with Metropolis-Hastings algorithm. Also, we give application with real data set to show the flexibility of the EWG distribution. Finally, summary and discussion are mentioned.

• The Korean Journal of Applied Statistics
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• v.22 no.3
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• pp.607-616
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• 2009

In many epidemiological studies, the occurrence times of the event of interest are right-censored or interval censored. In certain situations such as the AIDS data, however, the incubation period which is the time between HIV infection and the diagnosis of AIDS is usually doubly censored. In this paper, we impute the interval censored HIV infection time using three imputation methods. Mid imputation, conditional mean imputation and approximate Bayesian bootstrap are implemented to obtain right censored data, and then Gibbs sampler is used to estimate the coefficient factor of the incubation period. By using Bayesian approach, flexible modeling and the use of prior information is available. We applied both parametric and semi-parametric methods for estimating the effect of the covariate and compared the imputation results incorporating prior information for the covariate effects.

• Journal of the Korean Data and Information Science Society
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• v.27 no.1
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• pp.245-254
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• 2016

Many surveys provide categorical data and there may be one or more missing categories. We describe a nonignorable nonresponse model for the analysis of two-way contingency tables from small areas. There are both item and unit nonresponse. One approach to analyze these data is to construct several tables corresponding to missing categories. We describe a hierarchical Bayesian model to analyze two-way categorical data from different areas. This allows a "borrowing of strength" of the data from larger areas to improve the reliability in the estimates of the model parameters corresponding to the small areas. Also we use a nonignorable nonresponse model with Bayesian uncertainty analysis by placing priors in nonidentifiable parameters instead of a sensitivity analysis for nonidentifiable parameters. We use the griddy Gibbs sampler to fit our models and compute DIC and BPP for model diagnostics. We illustrate our method using data from NHANES III data on thirteen states to obtain the finite population proportions.