• Proceedings of the Korean Association for Survey Research Conference
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• 2006.06a
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• pp.131-159
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• 2006

This paper consider multinomial group testing which is concerned with classification each of N given units into one of k disjoint categories. In this paper, we propose exact Bayesian, approximate Bayesian, bootstrap methods for estimating individual category proportions using the multinomial group testing model proposed by Bar-Lev et al (2005). By the comparison of Mcan Squre Error (MSE), it is shown that the exact Bayesian method has a bettor efficiency and consistency than maximum likelihood method. We suggest an approximate Bayesian approach using Markov Chain Monte Carlo (MCMC) for posterior computation. We derive exact credible intervals based on the exact Bayesian estimators and present confidence intervals using the bootstrap and MCMC. These intervals arc shown to often have better coverage properties and similar mean lengths to maximum likelihood method already available. Furthermore the proposed models are illustrated using data from a HIV blooding test study throughout California, 2000.

• Communications for Statistical Applications and Methods
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• v.28 no.5
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• pp.425-445
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• 2021

A generalization of the log-logistic (LL) distribution called exponentiated log-logistic (ELL) distribution on lines of exponentiated Weibull distribution is considered. In this paper, based on progressive type-II censored samples, we have derived the maximum likelihood estimators and Bayes estimators for three parameters, the survival function and hazard function of the ELL distribution. Then, under the balanced squared error loss (BSEL) and the balanced linex loss (BLEL) functions, their corresponding Bayes estimators are obtained using Lindley's approximation (see Jung and Chung, 2018; Lindley, 1980), Tierney-Kadane approximation (see Tierney and Kadane, 1986) and Markov Chain Monte Carlo methods (see Hastings, 1970; Gelfand and Smith, 1990). Here, to check the convergence of MCMC chains, the Gelman and Rubin diagnostic (see Gelman and Rubin, 1992; Brooks and Gelman, 1997) was used. On the basis of their risks, the performances of their Bayes estimators are compared with maximum likelihood estimators in the simulation studies. In this paper, research supports the conclusion that ELL distribution is an efficient distribution to modeling data in the analysis of survival data. On top of that, Bayes estimators under various loss functions are useful for many estimation problems.

• Nuclear Engineering and Technology
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• v.54 no.8
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• pp.2941-2959
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• 2022

The fire brigade non-suppression probability model is a major factor that should be considered in evaluating fire-induced risk through fire probabilistic risk assessment (PRA), and also uncertainty is a critical consideration in support of risk-informed performance-based (RIPB) fire protection decision-making. This study developed an optimal integrated probabilistic fire brigade non-suppression model considering uncertainty of parameters based on the Bayesian Markov Chain Monte Carlo (MCMC) approach on electrical fire which is one of the most risk significant contributors. The result shows that the log-normal probability model with a location parameter (µ) of 2.063 and a scale parameter (σ) of 1.879 is best fitting to the actual fire experience data. It gives optimal model adequacy performance with Bayesian information criterion (BIC) of -1601.766, residual sum of squares (RSS) of 2.51E-04, and mean squared error (MSE) of 2.08E-06. This optimal log-normal model shows the better performance of the model adequacy than the exponential probability model suggested in the current fire PRA methodology, with a decrease of 17.3% in BIC, 85.3% in RSS, and 85.3% in MSE. The outcomes of this study are expected to contribute to the improvement and securement of fire PRA realism in the support of decision-making for RIPB fire protection programs.

• Journal of Korean Society for Quality Management
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• v.35 no.4
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• pp.159-165
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• 2007

Using statistical methods a change-point analysis of oil supply disruption is conducted. The statistical distribution of oil supply disruption is a weibull distribution. The detection of the change-point is applied to Bayesian method and weibull parameters are estimated through Markov chain monte carlo and parameter approach. The statistical approaches to the estimation for the change-point and weibull parameters is implemented with the sets of simulated and real data with small sizes of samples.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.4 no.1
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• pp.119-124
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• 2004

Real data as web log file tend to be incomplete. But we have to find useful knowledge from these for optimal decision. In web log data, many useful things which are hyperlink information and web usages of connected users may be found. The size of web data is too huge to use for effective knowledge discovery. To make matters worse, they are very sparse. We overcome this sparse problem using Markov Chain Monte Carlo method as multiple imputations. This missing value imputation changes spare web data to complete. Our study may be a useful tool for discovering knowledge from data set with sparseness. The more sparseness of data in increased, the better performance of MCMC imputation is good. We verified our work by experiments using UCI machine learning repository data.

• Journal of the Korea Institute of Building Construction
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• v.11 no.1
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• pp.91-99
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• 2011

Bayesian network is a form of probabilistic graphical model. It incorporates human reasoning to deal with sparse data availability and to determine the probabilities of uncertain cases. In this research, bayesian network is adopted to model the problem of construction project cost. General information, time, cost, and material, the four main factors dominating the characteristic of construction costs, are incorporated into the model. This research presents verify a model that were conducted to illustrate the functionality and application of a decision support system for predicting the costs. The Markov Chain Monte Carlo (MCMC) method is applied to estimate parameter distributions. Furthermore, it is shown that not all the parameters are normally distributed. In addition, cost estimates based on the Gibbs output is performed. It can enhance the decision the decision-making process.

• 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.

• Geophysics and Geophysical Exploration
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• v.5 no.4
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• pp.262-271
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• 2002

This study presents a practical procedure for the Bayesian inversion of geophysical data. We have applied geostatistical techniques for the acquisition of prior model information, then the Markov Chain Monte Carlo (MCMC) method was adopted to infer the characteristics of the marginal distributions of model parameters. For the Bayesian inversion of dipole-dipole array resistivity data, we have used the indicator kriging and simulation techniques to generate cumulative density functions from Schlumberger array resistivity data and well logging data, and obtained prior information by cokriging and simulations from covariogram models. The indicator approach makes it possible to incorporate non-parametric information into the probabilistic density function. We have also adopted the MCMC approach, based on Gibbs sampling, to examine the characteristics of a posteriori probability density function and the marginal distribution of each parameter.

• The Korean Journal of Applied Statistics
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• v.24 no.5
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• pp.951-961
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• 2011

In this paper, we propose a Bayesian inference using the Markov Chain Monte Carlo(MCMC) method for the zero inflated negative binomial(ZINB) regression model. The proposed model allows the regression model for zero inflation probability as well as the regression model for the mean of the dependent variable. This extends the work of Jang et al. (2010) to the fully defiend ZINB regression model. In addition, we apply the proposed method to a real data example, and compare the efficiency with the zero inflated Poisson model using the DIC. Since the DIC of the ZINB is smaller than that of the ZIP, the ZINB model shows superior performance over the ZIP model in zero inflated count data with overdispersion.

• Journal of Korea Water Resources Association
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• v.43 no.4
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• pp.337-351
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• 2010

There is a growing dissatisfaction with use of conventional statistical methods for the prediction of extreme events. Conventional methodology for modeling extreme event consists of adopting an asymptotic model to describe stochastic variation. However asymptotically motivated models remain the centerpiece of our modeling strategy, since without such an asymptotic basis, models have no rational for extrapolation beyond the level of observed data. Also, this asymptotic models ignored or overestimate the uncertainty and finally decrease the reliability of uncertainty. Therefore this article provide the research example of the extreme rainfall event and the methodology to reduce the uncertainty. In this study, the Bayesian MCMC (Bayesian Markov Chain Monte Carlo) and the MLE (Maximum Likelihood Estimation) methods using a quadratic approximation are applied to perform the at-site rainfall frequency analysis. Especially, the GEV distribution and Gumbel distribution which frequently used distribution in the fields of rainfall frequency distribution are used and compared. Also, the results of two distribution are analyzed and compared in the aspect of uncertainty.