• Journal of the Computational Structural Engineering Institute of Korea
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• v.30 no.1
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• pp.87-94
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• 2017

Reliability analysis(RA) and Reliability-based design optimization(RBDO) require statistical modeling of input random variables, which is parametrically or nonparametrically determined based on experimental data. For the parametric method, goodness-of-fit (GOF) test and model selection method are widely used, and a sequential statistical modeling method combining the merits of the two methods has been recently proposed. Kernel density estimation(KDE) is often used as a nonparametric method, and it well describes a distribution function when the number of data is small or a density function has multimodal distribution. Although accurate statistical models are needed to obtain accurate RA and RBDO results, accurate statistical modeling is difficult when the number of data is small. In this study, the accuracy of two statistical modeling methods, SSM and KDE, were compared according to the number of data. Through numerical examples, the RA results using the input models modeled by two methods were compared, and appropriate modeling method was proposed according to the number of data.

• Proceedings of the Korean Statistical Society Conference
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• 2003.10a
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• pp.179-182
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• 2003

This study describes a new graphical method for assessing and characterizing effect modification by a matching covariate in matched case-control studies. This method to understand effect modification is based on a semiparametric model using a varying coefficient model. The method allows for nonparametric relationships between effect modification and other covariates, or can be useful in suggesting parametric models. This method can be applied to examining effect modification by any ordered categorical or continuous covariates for which cases have been matched with controls. The method applies to effect modification when causality might be reasonably assumed. An example from veterinary medicine is used to demonstrate our approach. The simulation results show that this method, when based on linear, quadratic and nonparametric effect modification, can be more powerful than both a parametric multiplicative model fit and a fully nonparametric generalized additive model fit.

• Communications for Statistical Applications and Methods
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• v.27 no.5
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• pp.547-568
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• 2020

Modeling the statistical autocorrelations in spatial data is often achieved through the estimation of the variograms, where the selection of the appropriate valid variogram model, especially for small samples, is crucial for achieving precise spatial prediction results from kriging interpolations. To estimate such a variogram, we traditionally start by computing the empirical variogram (traditional Matheron or robust Cressie-Hawkins or kernel-based nonparametric approaches). In this article, we conduct numerical studies comparing the performance of these empirical variograms. In most situations, the nonparametric empirical variable nearest-neighbor (VNN) showed better performance than its competitors (Matheron, Cressie-Hawkins, and Nadaraya-Watson). The analysis of the spatial groundwater dataset used in this article suggests that the wave variogram model, with hole effect structure, fitted to the empirical VNN variogram is the most appropriate choice. This selected variogram is used with the ordinary kriging model to produce the predicted pollution map of the nitrate concentrations in groundwater dataset.

• Communications for Statistical Applications and Methods
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• v.22 no.6
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• pp.543-556
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• 2015

We present a survey of contributions that defined the nature and extent of robust statistics for the last 50 years. From the pioneering work of Tukey, Huber, and Hampel that focused on robust location parameter estimation, we presented various generalizations of these estimation procedures that cover a wide variety of models and data analysis methods. Among these extensions, we present linear models, clustered and dependent observations, times series data, binary and discrete data, models for spatial data, nonparametric methods, and forward search methods for outliers. We also present the current interest in robust statistics and conclude with suggestions on the possible future direction of this area for statistical science.

• Journal of the Korean Statistical Society
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• v.31 no.1
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• pp.63-75
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• 2002

Most attempts at Bayesian analysis of neural networks involve hierarchical modeling. We believe that similar results can be obtained with simpler models that require less computational effort, as long as appropriate restrictions are placed on parameters in order to ensure propriety of posterior distributions. In particular, we adopt a model first introduced by Lee (1999) that utilizes an improper prior for all parameters. Straightforward Gibbs sampling is possible, with the exception of the bias parameters, which are embedded in nonlinear sigmoidal functions. In addition to the problems posed by nonlinearity, direct sampling from the posterior distributions of the bias parameters is compounded due to the duplication of hidden nodes, which is a source of multimodality. In this regard, we focus on sampling from the marginal posterior distribution of the bias parameters with Markov chain Monte Carlo methods that combine traditional Metropolis sampling with a slice sampler described by Neal (1997, 2001). The methods are illustrated with data examples that are largely confined to the analysis of nonparametric regression models.

• The Korean Journal of Applied Statistics
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• v.29 no.4
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• pp.627-641
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• 2016

In this paper, we consider a seemingly unrelated regression (SUR) model and propose a nonparametric Bayesian approach to SUR with a Dirichlet process mixture of normals for modeling an unknown error distribution. Posterior distributions are derived based on the proposed model, and the posterior inference is performed via Markov chain Monte Carlo methods based on the collapsed Gibbs sampler of a Dirichlet process mixture model. We present a simulation study to assess the performance of the model. We also apply the model to precipitation data over South Korea.

• Communications for Statistical Applications and Methods
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• v.17 no.2
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• pp.141-151
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• 2010

Hybrid fuzzy regression analysis is used for integrating randomness and fuzziness into a regression model. Least squares support vector machine(LS-SVM) has been very successful in pattern recognition and function estimation problems for crisp data. This paper proposes a new method to evaluate hybrid fuzzy linear and nonlinear regression models with crisp inputs and fuzzy output using weighted fuzzy arithmetic(WFA) and LS-SVM. LS-SVM allows us to perform fuzzy nonlinear regression analysis by constructing a fuzzy linear regression function in a high dimensional feature space. The proposed method is not computationally expensive since its solution is obtained from a simple linear equation system. In particular, this method is a very attractive approach to modeling nonlinear data, and is nonparametric method in the sense that we do not have to assume the underlying model function for fuzzy nonlinear regression model with crisp inputs and fuzzy output. Experimental results are then presented which indicate the performance of this method.

• Communications for Statistical Applications and Methods
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• v.29 no.1
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• pp.65-83
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• 2022

Although various statistical methods have been developed to map time-dependent genetic factors, most identified genetic variants can explain only a small portion of the estimated genetic variation in longitudinal traits. Gene-gene and gene-time/environment interactions are known to be important putative sources of the missing heritability. However, mapping epistatic gene-gene interactions is extremely difficult due to the very large parameter spaces for models containing such interactions. In this paper, we develop a Gaussian process (GP) based nonparametric Bayesian variable selection method for longitudinal data. It maps multiple genetic markers without restricting to pairwise interactions. Rather than modeling each main and interaction term explicitly, the GP model measures the importance of each marker, regardless of whether it is mostly due to a main effect or some interaction effect(s), via an unspecified function. To improve the flexibility of the GP model, we propose a novel grid-based method for the within-subject dependence structure. The proposed method can accurately approximate complex covariance structures. The dimension of the covariance matrix depends only on the number of fixed grid points although each subject may have different numbers of measurements at different time points. The deviance information criterion (DIC) and the Bayesian predictive information criterion (BPIC) are proposed for selecting an optimal number of grid points. To efficiently draw posterior samples, we combine a hybrid Monte Carlo method with a partially collapsed Gibbs (PCG) sampler. We apply the proposed GP model to a mouse dataset on age-related body weight.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.32 no.1
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• pp.55-63
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• 2019

In engineering problems, many random variables have correlation, and the correlation of input random variables has a great influence on reliability analysis results of the mechanical systems. However, correlated variables are often treated as independent variables or modeled by specific parametric joint distributions due to difficulty in modeling joint distributions. Especially, when there are insufficient correlated data, it becomes more difficult to correctly model the joint distribution. In this study, multivariate kernel density estimation with bounded data is proposed to estimate various types of joint distributions with highly nonlinearity. Since it combines given data with bounded data, which are generated from confidence intervals of uniform distribution parameters for given data, it is less sensitive to data quality and number of data. Thus, it yields conservative statistical modeling and reliability analysis results, and its performance is verified through statistical simulation and engineering examples.

• 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.