• Journal of the Korean Society for Railway
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• v.19 no.4
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• pp.547-554
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• 2016

This study considered how to estimate the deterioration rate of the track quality index, which represents track geometric irregularity. Most existing studies have used a simple linear regression and regarded the slope of the regression equation as the progress rate. In this paper, we present a Bayesian approach to estimate the track irregularity progress. This Bayesian approach has many advantages, among which the biggest is that it can formally include the prior distribution of parameters which can be derived from historic data or from expert experiences; then, the rate can be expressed as a probability distribution. We investigated the possibility of applying the Bayesian method to the estimation of the deterioration rate by comparing our bayesian approach to the conventional linear regression approach.

• The Korean Journal of Applied Statistics
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• v.26 no.5
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• pp.737-746
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• 2013

The Bayesian method can be applied successfully to the estimation of the censored regression model introduced by Tobin (1958). The Bayes estimates show improvements over the maximum likelihood estimate; however, the performance of the Bayesian interval estimation is questionable. In Bayesian paradigm, the prior distribution usually reflects personal beliefs about the parameters. Such subjective priors will typically yield interval estimators with poor frequentist properties; however, an objective noninformative often yields a Bayesian procedure with good frequentist properties. We examine the performance of frequentist properties of noninformative priors for the Tobit regression model.

• The Korean Journal of Applied Statistics
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• v.27 no.6
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• pp.1049-1068
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• 2014

Autoregressive models are used to analyze an univariate time series data; however, these methods can be inappropriate when a structural break appears in a time series since they assume that a trend is consistent. Threshold autoregressive models (popular regime-switching models) have been proposed to address this problem. Recently, the models have been extended to two regime-switching models with delay parameter. We discuss two regime-switching threshold autoregressive models from a Bayesian point of view. For a Bayesian analysis, we consider a parametric threshold autoregressive model and a nonparametric threshold autoregressive model using Dirichlet process prior. The posterior distributions are derived and the posterior inferences is performed via Markov chain Monte Carlo method and based on two Bayesian threshold autoregressive models. We present a simulation study to compare the performance of the models. We also apply models to gross domestic product data of U.S.A and South Korea.

• The Korean Journal of Applied Statistics
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• v.34 no.3
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• pp.491-505
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• 2021

We consider linear regression models in high-dimensional settings (p ≫ n) and compare various classes of priors. The spike and slab prior is one of the most widely used priors for Bayesian regression models, but its model space is vast, resulting in a bad performance in finite samples. As an alternative, various continuous shrinkage priors, including the horseshoe prior and its variants, have been proposed. Although each of the above priors has been investigated separately, exhaustive comparative studies of their performance have been conducted very rarely. In this study, we compare the spike and slab prior, the horseshoe prior and its variants in various simulation settings. The performance of each method is demonstrated in terms of the regression coefficient estimation and variable selection. Finally, some remarks and suggestions are given based on comprehensive simulation studies.

• The Korean Journal of Applied Statistics
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• v.27 no.6
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• pp.867-889
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• 2014

Nonparametric Bayesian (np Bayes) statistical models are popularly used in a variety of research areas because of their flexibility and computational convenience. This paper reviews the np Bayes models focusing on biomedical research applications. We review key probability models for np Bayes inference while illustrating how each of the models is used to answer different types of research questions using biomedical examples. The examples are chosen to highlight the problems that are challenging for standard parametric inference but can be solved using nonparametric inference. We discuss np Bayes inference in four topics: (1) density estimation, (2) clustering, (3) random effects distribution, and (4) regression.

• The Korean Journal of Applied Statistics
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• v.35 no.3
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• pp.445-455
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• 2022

In this paper, we introduce existing Bayesian methods for high-dimensional sparse regression models and compare their performance in various simulation scenarios. Especially, we focus on the variational Bayes approach proposed by Ray and Szabó (2021), which enables scalable and accurate Bayesian inference. Based on simulated data sets from sparse high-dimensional linear regression models, we compare the variational Bayes approach with other Bayesian and frequentist methods. To check the practical performance of the variational Bayes in logistic regression models, a real data analysis is conducted using leukemia data set.

• The Korean Journal of Applied Statistics
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• v.35 no.2
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• pp.311-325
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• 2022

For count responses, the situation of excess zeros often occurs in various research fields. Zero-inflated model is a common choice for modeling such count data. Bayesian inference for the zero-inflated model has long been recognized as a hard problem because the form of conditional posterior distribution is not in closed form. Recently, however, Pillow and Scott (2012) and Polson et al. (2013) proposed a Pólya-Gamma data-augmentation strategy for logistic and negative binomial models, facilitating Bayesian inference for the zero-inflated model. We apply Bayesian zero-inflated negative binomial regression model to longitudinal pharmaceutical data which have been previously analyzed by Min and Agresti (2005). To facilitate posterior sampling for longitudinal zero-inflated model, we use the Pólya-Gamma data-augmentation strategy.

• The Korean Journal of Applied Statistics
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• v.21 no.4
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• pp.603-613
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• 2008

We often encounter the situation that discrete count data have a large portion of zeros. In this case, it is not appropriate to analyze the data based on standard regression models such as the poisson or negative binomial regression models. In this article, we consider Bayesian analysis for two commonly used models. They are zero-inflated poisson and negative binomial regression models. We use the Bayes factor as a model selection tool and computation is proceeded via Markov chain Monte Carlo methods. Crash count data are analyzed to support theoretical results.

• The Korean Journal of Applied Statistics
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• v.27 no.6
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• pp.991-1002
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• 2014

Both Bayesian and maximum likelihood methods are efficient for the estimation of regression coefficients of various Tobit regression models (see. e.g. Chib, 1992; Greene, 1990; Lee and Choi, 2013); however, some researchers recognized that the maximum likelihood method tends to underestimate the disturbance variance, which has implications for the estimation of marginal effects and the asymptotic standard error of estimates. The underestimation of the maximum likelihood estimate in a seemingly unrelated Tobit regression model is examined. A Bayesian method based on an objective noninformative prior is shown to provide proper estimates of the disturbance variance as well as other regression parameters

• 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.