• The Korean Journal of Applied Statistics
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• v.30 no.4
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• pp.579-590
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• 2017

The multivariate empirical distribution function could be defined when its distribution function can be estimated. It is known that bivariate empirical distribution functions could be visualized by using Step plot and Quantile plot. In this paper, the multivariate empirical distribution plot is proposed to represent the multivariate empirical distribution function on the unit square. Based on many kinds of empirical distribution plots corresponding to various multivariate normal distributions and other specific distributions, it is found that the empirical distribution plot also depends sensitively on its distribution function and correlation coefficients. Hence, we could suggest five goodness-of-fit test statistics. These critical values are obtained by Monte Carlo simulation. We explore that these critical values are not much different from those in text books. Therefore, we may conclude that the proposed test statistics in this work would be used with known critical values with ease.

• Geomechanics and Engineering
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• v.16 no.6
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• pp.655-667
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• 2018

To evaluate the stability of a rock slope with one pre-exiting vertical crack, this paper performs corresponding probabilistic stability analysis. The existence of cracks is generally ignored in traditional deterministic stability analysis. However, they are widely found in either cohesive soil or rock slopes. The influence of one pre-exiting vertical crack on a rock slope is considered in this study. The safety factor, which is usually adopted to quantity the stability of slopes, is derived through the deterministic computation based on the strength reduction technique. The generalized Hoek-Brown (HB) failure criterion is adopted to characterize the failure of rock masses. Considering high nonlinearity of the limit state function as using nonlinear HB criterion, the multivariate adaptive regression splines (MARS) is used to accurately approximate the implicit limit state function of a rock slope. Then the MARS is integrated with Monte Carlo simulation to implement reliability analysis, and the influences of distribution types, level of uncertainty, and constants on the probability density functions and failure probability are discussed. It is found that distribution types of random variables have little influence on reliability results. The reliability results are affected by a combination of the uncertainty level and the constants. Finally, a reliability-based design figure is provided to evaluate the safety factor of a slope required for a target failure probability.

• KIISE Transactions on Computing Practices
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• v.21 no.1
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• pp.94-99
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• 2015

With the recent machine learning paradigm of using nonparametric Bayesian statistics and statistical inference based on random sampling, the Dirichlet distribution finds many uses in a variety of graphical models. It is a multivariate generalization of the gamma distribution and is defined on a continuous (K-1)-simplex. This paper presents a sampling method for a Dirichlet distribution for the problem of dividing an integer X into a sequence of K integers which sum to X. The target samples in our problem are all positive integer vectors when multiplied by a given X. They must be sampled from the correspondingly gridded simplex. In this paper we develop a Markov Chain Monte Carlo (MCMC) proposal distribution for the neighborhood grid points on the simplex and then present the complete algorithm based on the Metropolis-Hastings algorithm. The proposed algorithm can be used for the Markov model, HMM, and Semi-Markov model for accurate state-duration modeling. It can also be used for the Gamma-Dirichlet HMM to model q the global-local duration distributions.

• The Korean Journal of Applied Statistics
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• v.29 no.1
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• pp.99-112
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• 2016

Asymmetric jump-diffusion models are effectively used to model the dynamic behavior of asset prices with abrupt asymmetric upward and downward changes. However, the estimation of their extension to the multivariate asymmetric jump-diffusion model has been hampered by the analytically intractable likelihood function. This article confronts the problem using a data augmentation method and proposes a new Bayesian method for a multivariate asymmetric Laplace jump-diffusion model. Unlike the previous models, the proposed model is rich enough to incorporate all possible correlated jumps as well as mention individual and common jumps. The proposed model and methodology are illustrated with a simulation study and applied to daily returns for the KOSPI, S&P500, and Nikkei225 indices data from January 2005 to September 2015.

• Proceedings of the Korea Water Resources Association Conference
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• 2009.05a
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• pp.540-544
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• 2009

Hydrologic pattern under climate change has been paid attention to as one of the most important issues in hydrologic science group. Rainfall and runoff is a key element in the Earth's hydrological cycle, and associated with many different aspects such as water supply, flood prevention and river restoration. In this regard, a main objective of this study is to evaluate design flood using simulation techniques which can consider a full spectrum of uncertainty. Here we utilize a weather state based stochastic multivariate model as conditional probability model for simulating the rainfall field. A major premise of this study is that large scale climatic patterns are a major driver of such persistent year to year changes in rainfall probabilities. Uncertainty analysis in estimating design flood is inevitably needed to examine reliability for the estimated results. With regard to this point, this study applies a Bayesian Markov Chain Monte Carlo scheme to the NWS-PC rainfall-runoff model that has been widely used, and a case study is performed in Soyang Dam watershed in Korea. A comprehensive discussion on design flood under climate change is provided.

• Proceedings of the Korean Statistical Society Conference
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• 2003.10a
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• pp.9-14
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• 2003

A Bayesian model-based clustering method is proposed for clustering objects on the basis of dissimilarites. This combines two basic ideas. The first is that tile objects have latent positions in a Euclidean space, and that the observed dissimilarities are measurements of the Euclidean distances with error. The second idea is that the latent positions are generated from a mixture of multivariate normal distributions, each one corresponding to a cluster. We estimate the resulting model in a Bayesian way using Markov chain Monte Carlo. The method carries out multidimensional scaling and model-based clustering simultaneously, and yields good object configurations and good clustering results with reasonable measures of clustering uncertainties. In the examples we studied, the clustering results based on low-dimensional configurations were almost as good as those based on high-dimensional ones. Thus tile method can be used as a tool for dimension reduction when clustering high-dimensional objects, which may be useful especially for visual inspection of clusters. We also propose a Bayesian criterion for choosing the dimension of the object configuration and the number of clusters simultaneously. This is easy to compute and works reasonably well in simulations and real examples.

• Communications for Statistical Applications and Methods
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• v.16 no.1
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• pp.75-83
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• 2009

Parallelism tests are proposed for slope in the simple linear regression models. In this paper, we suggest the parametric test using HSD testing method (Tukey,1953) and distribution-free test using Kruskal-wallis (1952) for more than three slopes. Monte Carlo simulation study is adapted to compare the power of the proposed methods with Wilks' Lambda multivariate procedure.

• Communications for Statistical Applications and Methods
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• v.20 no.6
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• pp.439-454
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• 2013

This study presents a Bayesian multiple change-point detection approach to segment and classify the observations that no longer come from an initial population after a certain time. Inferences are based on the multiple change-points in a sequence of random variables where the probability distribution changes. Bayesian multiple change-point estimation is classifies each observation into a segment. We use a truncated Poisson distribution for the number of change-points and conjugate prior for the exponential family distributions. The Bayesian method can lead the unsupervised classification of discrete, continuous variables and multivariate vectors based on latent class models; therefore, the solution for change-points corresponds to the stochastic partitions of observed data. We demonstrate segmentation with real data.

• Journal of the Korean Data and Information Science Society
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• v.24 no.1
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• pp.189-200
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• 2013

In this paper, it will be assumed that there are two distinct populations which are multivariate normal with equal covariance matrix. We also assume that the two populations are equally likely and the costs of misclassification are equal. The classification rule depends on the situation whether the training samples include missing values or not. We consider the conditional bootstrap confidence intervals for classification error rate when a block of observation is missing.

• Wind and Structures
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• v.27 no.5
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• pp.283-291
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• 2018

This study presents the reliability assessment of a 100.5 m tall reinforced concrete chimney at a glass factory under wind loading by using vibration-based identified modal values. Ambient vibration measurements were recorded and modal values such as frequencies, shapes and damping ratios were identified by using Enhanced Frequency Domain Decomposition (EFDD) method. Afterwards, Finite Element Model (FEM) of the chimney was verified based on identified modal parameters. Reliability assessment of the chimney under wind loading was performed by obtaining the exceedance probability of demand to capacity distribution. Demand distribution of the chimney was developed under repetitive seeds of multivariate stochastic wind fields generated along the height of chimney. Capacity distribution of the chimney was developed by Monte Carlo simulation. Finally, it was found that reliability of the chimney is lower than code suggested limit values.