• The Korean Journal of Applied Statistics
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• v.22 no.1
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• pp.197-204
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• 2009

In the model selection problem, the main objective is to choose the true model from a manageable set of candidate models. An information criterion gauges the validity of a statistical model and judges the balance between goodness-of-fit and parsimony; "how well observed values ran approximate to the true values" and "how much information can be explained by the lower dimensional model" In this study, we introduce some information criteria modified from the Akaike Information Criterion (AIC) and the Bayesian Information Criterion(BIC). The information criteria considered in this study are compared via simulation studies and real application.

• Journal of the Korean Data and Information Science Society
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• v.26 no.3
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• pp.749-754
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• 2015

This article presents Bayesian approach to regression splines with knots on a grid of equally spaced sample quantiles of the independent variables under functional measurement error model.We consider small area model by using penalized splines of non-linear pattern. Specifically, in a basis functions of the regression spline, we use radial basis functions. To fit the model and estimate parameters we suggest a hierarchical Bayesian framework using Markov Chain Monte Carlo methodology. Furthermore, we illustrate the method in an application data. We check the convergence by a potential scale reduction factor and we use the posterior predictive p-value and the mean logarithmic conditional predictive ordinate to compar models.

• 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.

• Communications for Statistical Applications and Methods
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• v.8 no.2
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• pp.407-416
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• 2001

Sample surveys are usually designed and analyzed to produce estimates for a large area or populations. Therefore, for the small area estimations, sample sizes are often not large enough to give adequate precision. Several small area estimation methods were proposed in recent years concerning with sample sizes. Here, we will compare simple Bayesian approach with Bayesian prediction for small area estimation based on linear regression model. The performance of the proposed method was evaluated through unemployment population data form Economic Active Population(EAP) Survey.

• Communications for Statistical Applications and Methods
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• v.24 no.6
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• pp.673-683
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• 2017

The least absolute shrinkage and selection operator (LASSO) has been a popular regression estimator with simultaneous variable selection. However, LASSO does not have the oracle property and its robust version is needed in the case of heavy-tailed errors or serious outliers. We propose a robust penalized regression estimator which provide a simultaneous variable selection and estimator. It is based on the rank regression and the non-convex penalty function, the smoothly clipped absolute deviation (SCAD) function which has the oracle property. The proposed method combines the robustness of the rank regression and the oracle property of the SCAD penalty. We develop an efficient algorithm to compute the proposed estimator that includes a SCAD estimate based on the local linear approximation and the tuning parameter of the penalty function. Our estimate can be obtained by the least absolute deviation method. We used an optimal tuning parameter based on the Bayesian information criterion and the cross validation method. Numerical simulation shows that the proposed estimator is robust and effective to analyze contaminated data.

• The Journal of the Korea Contents Association
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• v.21 no.11
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• pp.77-86
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• 2021

A method of constructing a war simulation based on Bayesian Inference was proposed as a method of constructing heterogeneous historical war data obtained with a time difference into a single model. A method of applying a linear regression model can be considered as a method of predicting future battles by analyzing historical war results. However it is not appropriate for two heterogeneous types of historical data that reflect changes in the battlefield environment due to different times to be suitable as a single linear regression model and violation of the model's assumptions. To resolve these problems a Bayesian inference method was proposed to obtain a post-distribution by assuming the data from the previous era as a non-informative prior distribution and to infer the final posterior distribution by using it as a prior distribution to analyze the data obtained from the next era. Another advantage of the Bayesian inference method is that the results sampled by the Markov Chain Monte Carlo method can be used to infer posterior distribution or posterior predictive distribution reflecting uncertainty. In this way, it has the advantage of not only being able to utilize a variety of information rather than analyzing it with a classical linear regression model, but also continuing to update the model by reflecting additional data obtained in the future.

• Journal of Korean Society for Quality Management
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• v.26 no.4
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• pp.151-165
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• 1998

Consider the linear multivariate regression model $Y=X_1B_1＋X_2B_2＋U$, where Vec(U)~N(0, $\sum \bigotimes I_N$). This paper is concerned with Bayes infreence of the model when it is suspected that the elements of $B_2$ are constrained in the form of intervals. The use of the Gibbs sampler as a method for calculating Bayesian marginal posterior desnities of the parameters under a generalized conjugate prior is developed. It is shown that the a, pp.oach is straightforward to specify distributionally and to implement computationally, with output readily adopted for required inference summaries. The method developed is a, pp.ied to a real problem.

• The Journal of Asian Finance, Economics and Business
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• v.8 no.4
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• pp.665-672
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• 2021

The paper examines the impact of shadow economy and corruption, along with public expenditure, trade openness, foreign direct investment (FDI), inflation, and tax revenue on the economic growth of the BRICS countries. Data were collected from the World Bank, Transparency International, and Heritage Foundation over the 1991-2017 period. The Bayesian linear regression method is used to examine whether shadow economy, corruption and other indicators affect the economic growth of countries studied. This paper applies the normal prior suggested by Lemoine (2019) while the posterior distribution is simulated using Monte Carlo Markov Chain (MCMC) technique through the Gibbs sampling algorithm. The results indicate that public expenditure and trade openness can enhance the BRICS countries' economic growth, with the positive impact probability of 75.69% and 67.11%, respectively. Also, FDI, inflation, and tax revenue positively affect this growth, though the probability of positive effect is ambiguous, ranging from 51.13% to 56.36%. Further, the research's major finding is that shadow economy and control of corruption have a positive effect on the economic growth of the BRICS countries. Nevertheless, the posterior probabilities of these two factors are 62.23% and 65.25%, respectively. This result suggests that their positive effect probability is not high.

• Journal of the Korean Statistical Society
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• v.22 no.2
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• pp.209-217
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• 1993

The multicollinearity problem in a multiple linear regression model may present deleterious effects on predictions. Thus, its is desirable to consider the optimal fractions with respect to the unbiased estimate of the mean squares errors of the predicted values. Interstingly, the optimal fractions can be also illuminated by the Bayesian inerpretation of the general James-Stein estimators.

• Journal of Korea Artificial Intelligence Association
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• v.1 no.1
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• pp.11-16
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• 2023

Accurate hospital case modeling and prediction are crucial for efficient healthcare. In this study, we demonstrate the implementation of regression analysis methods in machine learning systems utilizing mathematical statics and machine learning techniques. The developed machine learning model includes Bayesian linear, artificial neural network, decision tree, decision forest, and linear regression analysis models. Through the application of these algorithms, corresponding regression models were constructed and analyzed. The results suggest the potential of leveraging machine learning systems for medical research. The experiment aimed to create an Azure Machine Learning Studio tool for the speedy evaluation of multiple regression models. The tool faciliates the comparision of 5 types of regression models in a unified experiment and presents assessment results with performance metrics. Evaluation of regression machine learning models highlighted the advantages of boosted decision tree regression, and decision forest regression in hospital case prediction. These findings could lay the groundwork for the deliberate development of new directions in medical data processing and decision making. Furthermore, potential avenues for future research may include exploring methods such as clustering, classification, and anomaly detection in healthcare systems.