• Communications for Statistical Applications and Methods
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• v.19 no.6
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• pp.885-898
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• 2012

In this paper, we consider Bayesian approaches to partially linear models, in which a regression function is represented by a semiparametric additive form of a parametric linear regression function and a nonparametric regression function. We make a comparative study on the performance of widely used Bayesian partially linear models in terms of empirical analysis. Specifically, we deal with three Bayesian methods to estimate the nonparametric regression function, one method using Fourier series representation, the other method based on Gaussian process regression approach, and the third method based on the smoothness of the function and differencing. We compare the numerical performance of three methods by the root mean squared error(RMSE). For empirical analysis, we consider synthetic data with simulation studies and real data application by fitting each of them with three Bayesian methods and comparing the RMSEs.

• 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.

• Communications for Statistical Applications and Methods
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• v.22 no.4
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• pp.349-359
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• 2015

We study a semiparametric Bayesian approach to small area estimation under a nested error linear regression model with area level covariate subject to measurement error. Consideration is given to radial basis functions for the regression spline and knots on a grid of equally spaced sample quantiles of covariate with measurement errors in the nested error linear regression model setup. We conduct a hierarchical Bayesian structural measurement error model for small areas and prove the propriety of the joint posterior based on a given hierarchical Bayesian framework since some priors are defined non-informative improper priors that uses Markov Chain Monte Carlo methods to fit it. Our methodology is illustrated using numerical examples to compare possible models based on model adequacy criteria; in addition, analysis is conducted based on real data.

• Journal of the Korean Data and Information Science Society
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• v.9 no.2
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• pp.165-172
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• 1998

This paper considers a linear regression model with censored data where each error term follows a multivariate normal distribution. In this paper we consider the diffuse prior distribution for parameters of the linear regression model. With censored data we derive the full conditional densities for parameters of a multiple regression model in order to obtain the marginal posterior densities of the relevant parameters through the Gibbs Sampler, which was proposed by Geman and Geman(1984) and utilized by Gelfand and Smith(1990) with statistical viewpoint.

• Communications for Statistical Applications and Methods
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• v.27 no.2
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• pp.189-199
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• 2020

This paper studies a Bayesian ordered multiple linear regression model with skew normal error. It is reasonable that the kind of inherent information available in an applied regression requires some constraints on the coefficients to be estimated. In addition, the assumption of normality of the errors is sometimes not appropriate in the real data. Therefore, to explain such situations more flexibly, we use the skew-normal distribution given by Sahu et al. (The Canadian Journal of Statistics, 31, 129-150, 2003) for error-terms including normal distribution. For Bayesian methodology, the Markov chain Monte Carlo method is employed to resolve complicated integration problems. Also, under the improper priors, the propriety of the associated posterior density is shown. Our Bayesian proposed model is applied to NZAPB's apple data. For model comparison between the skew normal error model and the normal error model, we use the Bayes factor and deviance information criterion given by Spiegelhalter et al. (Journal of the Royal Statistical Society Series B (Statistical Methodology), 64, 583-639, 2002). We also consider the problem of detecting an influential point concerning skewness using Bayes factors. Finally, concluding remarks are discussed.

• Communications for Statistical Applications and Methods
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• v.28 no.2
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• pp.189-204
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• 2021

In a regression analysis, a single best model is usually selected among several candidate models. However, it is often useful to combine several candidate models to achieve better performance, especially, in the prediction viewpoint. Model combining methods such as stacking and Bayesian model averaging (BMA) have been suggested from the perspective of averaging candidate models. When the candidate models include a true model, it is expected that BMA generally gives better performance than stacking. On the other hand, when candidate models do not include the true model, it is known that stacking outperforms BMA. Since stacking and BMA approaches have different properties, it is difficult to determine which method is more appropriate under other situations. In particular, it is not easy to find research papers that compare stacking and BMA when regression model assumptions are violated. Therefore, in the paper, we compare the performance among model averaging methods as well as a single best model in the linear regression analysis when standard linear regression assumptions are violated. Simulations were conducted to compare model averaging methods with the linear regression when data include outliers and data do not include them. We also compared them when data include errors from a non-normal distribution. The model averaging methods were applied to the water pollution data, which have a strong multicollinearity among variables. Simulation studies showed that the stacking method tends to give better performance than BMA or standard linear regression analysis (including the stepwise selection method) in the sense of risks (see (3.1)) or prediction error (see (3.2)) when typical linear regression assumptions are violated.

• Journal of the Korean Statistical Society
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• v.28 no.3
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• pp.311-324
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• 1999

The problem of 'outliers', observations which look suspicious in some way, has long been one of the most concern in the statistical structure to experimenters and data analysts. We propose a model for an outlier problem and also analyze it in linear regression model using a Bayesian approach. Then we use the mean-shift model and SSVS(George and McCulloch, 1993)'s idea which is based on the data augmentation method. The advantage of proposed method is to find a subset of data which is most suspicious in the given model by the posterior probability. The MCMC method(Gibbs sampler) can be used to overcome the complicated Bayesian computation. Finally, a proposed method is applied to a simulated data and a real data.

• Communications for Statistical Applications and Methods
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• v.8 no.3
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• pp.805-814
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• 2001

The problem of 'outliers', observations which look suspicious in some way, has long been one of the most concern in the statistical structure to experimenters and data analysts. We propose a model for outliers problem and also analyze it in linear regression model using a Bayesian approach with the variance-inflation model. We will use Geweke's(1996) ideas which is based on the data augmentation method for detecting outliers in linear regression model. The advantage of the proposed method is to find a subset of data which is most suspicious in the given model by the posterior probability The sampling based approach can be used to allow the complicated Bayesian computation. Finally, our proposed methodology is applied to a simulated and a real data.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.6 no.4
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• pp.277-281
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• 2006

Cyber counseling, one of the most compatible type of consultation for the information society, enables people to reveal their mental agonies and private problems anonymously, since it does not require face-to-face interview between a counsellor and a client. However, there are few cyber counseling centers which provide high quality and trustworthy service, although the number of cyber counseling center has highly increased. Therefore, this paper is intended to enable an appropriate consultation for each client by analyzing client propensity using Bayesian variable selection. Bayesian variable selection is superior to stepwise regression analysis method in finding out a regression model. Stepwise regression analysis method, which has been generally used to analyze individual propensity in linear regression model, is not efficient since it is hard to select a proper model for its own defects. In this paper, based on the case database of current cyber counseling centers in the web, we will analyze clients' propensities using Bayesian variable selection to enable individually target counseling and to activate cyber counseling programs.

• The Korean Journal of Applied Statistics
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• v.15 no.1
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• pp.73-84
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• 2002

Linear regression models with inequality constraints on the coefficients are frequently used in economic models due to sign or order constraints on the coefficients. In this paper, we propose a Bayesian approach to selecting significant explanatory variables in linear regression models with inequality constraints on the coefficients. Bayesian variable selection requires computation of posterior probability of each candidate model. We propose a method which computes all the necessary posterior model probabilities simultaneously. In specific, we obtain posterior samples form the most general model via Gibbs sampling algorithm (Gelfand and Smith, 1990) and compute the posterior probabilities by using the samples. A real example is given to illustrate the method.