• Communications for Statistical Applications and Methods
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• v.1 no.1
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• pp.94-101
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• 1994

본 논문은 패널(panel) 자기회귀 모형에서 자기회귀 계수의 추정을 베이지안 방법으로 접근하였는데, 이 때 특별히 Gibbs Sampling 방법을 이용하여 사후분포를 계산하였다. 또한 모의 실험을 통하여 자기회귀계수를 Gibbs Sampling 방법으로 추정한 베이지안 추정치가 non-Bayesian 방법으로 구한 추정치보다 더 우월함을 보였다.

• 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.

• 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.

• The Korean Journal of Applied Statistics
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• v.31 no.5
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• pp.573-585
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• 2018

In this study, we fit the logistic regression model and naïve Bayesian classifier model using 11 risk factors to predict the incidence rate probability for type 2 diabetes mellitus. We then introduce how to construct a nomogram that can help people visually understand it. We use data from the 2013-2015 Korean National Health and Nutrition Examination Survey (KNHANES). We take 3 interactions in the logistic regression model to improve the quality of the analysis and facilitate the application of the left-aligned method to the Bayesian nomogram. Finally, we compare the two nomograms and examine their utility. Then we verify the nomogram using the ROC curve.

• The Korean Journal of Applied Statistics
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• v.24 no.2
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• pp.293-305
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• 2011

The volatility is one of most important parameters in the areas of pricing of financial derivatives an measuring risks arising from a sudden change of economic circumstance. We propose a Bayesian approach to estimate the volatility varying with time under a linear model with ARMA(p, q)-GARCH(r, s) errors. This Bayesian estimate of the volatility is compared with the ML estimate. We also present the probability of existence of the unit root in the GARCH model.

• 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.

• 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.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.15 no.1
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• pp.139-151
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• 2002

This study is concerned with model selection and diagnostics for nonlinear regression model through Bayes factor. In this paper, we use informative prior and simulate observations from the posterior distribution via Markov chain Monte Carlo. We propose the Laplace approximation method and apply the Laplace-Metropolis estimator to solve the computational difficulty of Bayes factor.

• 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.