• 한국데이터정보과학회:학술대회논문집
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• 2005.04a
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• pp.83-126
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• 2005

Single-index models have found applications in econometrics and biometrics, where multidimensional regression models are often encountered. Here we propose a nonparametric estimation approach that combines wavelet methods for non-equispaced designs with Bayesian models. We consider a wavelet series expansion of the unknown regression function and set prior distributions for the wavelet coefficients and the other model parameters. To ensure model identifiability, the direction parameter is represented via its polar coordinates. We employ ad hoc hierarchical mixture priors that perform shrinkage on wavelet coefficients and use Markov chain Monte Carlo methods for a posteriori inference. We investigate an independence-type Metropolis-Hastings algorithm to produce samples for the direction parameter. Our method leads to simultaneous estimates of the link function and of the index parameters. We present results on both simulated and real data, where we look at comparisons with other methods.

• Journal of Korean Society on Water Environment
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• v.36 no.4
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• pp.300-313
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• 2020

The Bayesian approach can be used to estimate hydrologic model parameters from the prior expert knowledge about the parameter values and the observed data. The purpose of this study was to compare the performance of the two Bayesian methods, the Metropolis-Hastings (MH) algorithm and the Generalized Likelihood Uncertainty Estimation (GLUE) method. These two methods were applied to the TANK model, a hydrological model comprising 13 parameters, to examine the uncertainty of the parameters of the model. The TANK model comprises a combination of multiple reservoir-type virtual vessels with orifice-type outlets and implements a common major hydrological process using the runoff calculations that convert the rainfall to the flow. As a result of the application to the Nam River A watershed, the two Bayesian methods yielded similar flow simulation results even though the parameter estimates obtained by the two methods were of somewhat different values. Both methods ensure the model's prediction accuracy even when the observed flow data available for parameter estimation is limited. However, the prediction accuracy of the model using the MH algorithm yielded slightly better results than that of the GLUE method. The flow duration curve calculated using the limited observed flow data showed that the marginal reliability is secured from the perspective of practical application.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.17 no.5
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• pp.645-652
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• 2016

The statistical modeling of input random variables is necessary in reliability analysis, reliability-based design optimization, and statistical validation and calibration of analysis models of mechanical systems. In statistical modeling methods, there are the Akaike Information Criterion (AIC), AIC correction (AICc), Bayesian Information Criterion, Maximum Likelihood Estimation (MLE), and Bayesian method. Those methods basically select the best fitted distribution among candidate models by calculating their likelihood function values from a given data set. The number of data or parameters in some methods are considered to identify the distribution types. On the other hand, the engineers in a real field have difficulties in selecting the statistical modeling method to obtain a statistical model of the experimental data because of a lack of knowledge of those methods. In this study, commonly used statistical modeling methods were compared using statistical simulation tests. Their advantages and disadvantages were then analyzed. In the simulation tests, various types of distribution were assumed as populations and the samples were generated randomly from them with different sample sizes. Real engineering data were used to verify each statistical modeling method.

• Communications for Statistical Applications and Methods
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• v.15 no.3
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• pp.379-386
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• 2008

In this paper, the choice of a primary resolution and wavelet basis functions are introduced under random or irregular design points of which the sample size is free of a power of two. Most wavelet methods have used the number of the points as the primary resolution. However, it turns out that a proper primary resolution is much affected by the shape of an unknown function. The proposed methods are illustrated by some simulations.

• The Korean Journal of Applied Statistics
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• v.20 no.2
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• pp.229-244
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• 2007

Among the small area estimation methods, it has been known that hierarchical Bayesian(HB) approach is the most reasonable and effective method. However any model based approaches need good explanatory variables and finding them is the key role in the model based approach. As the lacking of explanatory variables, adopting the spatial terms in the model was introduced. Here in this paper, we evaluate the model based methods with/without spatial terms using the diagnostic methods which were introduced by Brown et al. (2001). And Economic Active Population Survey(2005) is used for data analysis.

• Communications for Statistical Applications and Methods
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• v.27 no.1
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• pp.109-128
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• 2020

A climate-impact projection usually consists of several stages, and the uncertainty of the projection is known to be quite large. It is necessary to assess how much each stage contributed to the uncertainty. We call an uncertainty quantification method in which relative contribution of each stage can be evaluated as uncertainty decomposition. We propose a new Bayesian model for uncertainty decomposition in climate change impact assessments. The proposed Bayesian model can incorporate uncertainty of natural variability and utilize data in control period. We provide a simple and efficient Gibbs sampling algorithm using the auxiliary variable technique. We compare the proposed method with other existing uncertainty decomposition methods by analyzing streamflow data for Yongdam Dam basin located at Geum River in South Korea.

• Communications for Statistical Applications and Methods
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• v.6 no.3
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• pp.801-812
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• 1999

Change-point hazard rate models arise for example in applying "burn-in" techniques to screen defective items and in studing times until undesirable side effects occur in clinical trials. Sometimes in screening defectives it might be sensible to model two stages of burn-in. In a clinical trial there might be an initial hazard rate for a side effect which after a period of time changes to an intermediate hazard rate before settling into a long term hazard rate. In this paper we consider the multiple change points hazard rate model. The classical approach's asymptotics can be poor for the small to all moderate sample sizes often encountered in practice. We propose a Bayesian approach avoiding asymptotics to provide more reliable inference conditional only upon the data actually observed. The Bayesian models can be fitted using simulation methods. Model comparison is made using recently developed Bayesian model selection criteria. The above methodology is applied to a generated data and to a generated data and the Lawless(1982) failure times of electrical insulation.

• Journal of Korean Society for Quality Management
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• v.37 no.4
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• pp.16-22
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• 2009

The inflection S-shaped software reliability growth model (SRGM) proposed by Ohba(1984) is one of the most commonly used models and has been discussed by many authors. The main purpose of this paper is to estimate the parameters of Ohba's SRGM within the Bayesian framework by applying the Markov chain Monte Carlo techniques. While the maximum likelihood estimates for these parameters are well known, the Bayesian method for the inflection S-shaped SRGM have not been discussed in the literature. The proposed methods can be quite flexible depending on the choice of prior distributions for the parameters of interests. We also compare the Bayesian methods with the maximum likelihood method numerically based on the real data.

• Communications for Statistical Applications and Methods
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• v.29 no.1
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• pp.27-40
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• 2022

In this paper, the focus on the removal noise in the binary image based on the variational Bayesian method with the Ising model. The observation and the latent variable are the degraded image and the original image, respectively. The posterior distribution is built using the Markov random field and the Ising model. Estimating the posterior distribution is the same as reconstructing a degraded image. MCMC and variational Bayesian inference are two methods for estimating the posterior distribution. However, for the sake of computing efficiency, we adapt the variational technique. When the image is restored, the iterative method is used to solve the recursive problem. Since there are three model parameters in this paper, restoration is implemented using the VECM algorithm to find appropriate parameters in the current state. Finally, the restoration results are shown which have maximum peak signal-to-noise ratio (PSNR) and evidence lower bound (ELBO).

• Communications for Statistical Applications and Methods
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• v.24 no.1
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• pp.67-80
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• 2017

Over the last few decades, ensemble forecasts based on global climate models have become an important part of climate forecast due to the ability to reduce uncertainty in prediction. Moreover in ensemble forecast, assessing the prediction uncertainty is as important as estimating the optimal weights, and this is achieved through a probabilistic forecast which is based on the predictive distribution of future climate. The Bayesian model averaging has received much attention as a tool of probabilistic forecasting due to its simplicity and superior prediction. In this paper, we propose a new Bayesian model averaging method for probabilistic ensemble forecasting. The proposed method combines a deterministic ensemble forecast based on a multivariate regression approach with Bayesian model averaging. We demonstrate that the proposed method is better in prediction than the standard Bayesian model averaging approach by analyzing monthly average precipitations and temperatures for ten cities in Korea.