• The Korean Journal of Applied Statistics
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• v.16 no.2
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• pp.273-282
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• 2003

The problem of estimating the parameters of k-population Weibull distributions is discussed under the prior of ordered scale parameters. Parameters are estimated by the Gibbs sampling method. Since the conditional posterior distribution of the shape parameter in the Gibbs sampler is not log-concave, the shape parameter is generated by the adaptive rejection sampling. Finally, we applied this estimation methodology to the data discussed in Nelson (1970).

• The Korean Journal of Applied Statistics
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• v.13 no.2
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• pp.505-514
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• 2000

A Markov Chain Monte Carlo method with data augmentation is developed to compute the features of the posterior distribution. For each observed failure epoch, we introduced mixture failure model of Rayleigh and Erlang(2) pattern. This data augmentation approach facilitates specification of the transitional measure in the Markov Chain. Gibbs steps are proposed to perform the Bayesian inference of such models. For model determination, we explored sum of relative error criterion that selects the best model. A numerical example with simulated data set is given.

• The Korean Journal of Applied Statistics
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• v.26 no.5
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• pp.713-723
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• 2013

An objective Bayesian estimation procedure of the two-parameter Pareto distribution is presented under the reference prior and the noninformative prior. Bayesian estimators are obtained by Gibbs sampling. The steps to generate parameters in the Gibbs sampler are from the shape parameter of the gamma distribution and then the scale parameter by the adaptive rejection sampling algorism. A numerical study shows that the proposed objective Bayesian estimation outperforms other estimations in simulated bias and mean squared error.

• Journal of the Korean Data and Information Science Society
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• v.10 no.1
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• pp.119-133
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• 1999

A Markov Chain Monte Carlo method is developed to compute the software reliability model. We consider computation problem for determining of posterior distibution in Bayseian inference. Metropolis algorithms along with Gibbs sampling are proposed to preform the Bayesian inference of the Mixed model with record value statistics. For model determiniation, we explored the prequential conditional predictive ordinate criterion that selects the best model with the largest posterior likelihood among models using all possible subsets of the component intensity functions. To relax the monotonic intensity function assumptions. A numerical example with simulated data set is given.

• Communications for Statistical Applications and Methods
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• v.16 no.1
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• pp.31-40
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• 2009

Spatial time series data can be viewed either as a set of time series collected simultaneously at a number of spatial locations. In this paper, We estimate the parameters of spatial time autoregressive moving average (SIARMA) process by method of Gibbs sampling. Finally, We apply this method to a set of U.S. Mumps data over a 12 states region.

• The Korean Journal of Applied Statistics
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• v.17 no.2
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• pp.281-301
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• 2004

In this paper we consider the change point problem in a sequence of univariate normal observations. We want to know whether there is any change point or not. In case a change point exists, we will identify its change type. Namely, it can be a mean change, a variance change, or both the mean and variance change. The intrinsic Bayes factors of Berger and Pericchi (1996, 1998) are used to find the type of optimal change model. The Gibbs sampling including the Metropolis-Hastings algorithm is used to estimate all the parameters in the change model. These methods are checked via simulation and applied to the winter average temperature data in Seoul.

• Journal of Korean Society for Quality Management
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• v.26 no.1
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• pp.88-98
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• 1998

Process capability indices are used to determine whether a production process is capable of producing items within a specified tolerance. Using conditional distribution, we study some process capability indices ${\hat{C}}_{Gp}$, ${\hat{C}}_{Gpk}$, ${\hat{C}}_{Gpm}$ under conjugate prior distribution. We consider some process capability indices with Gibbs sampling method. Also, we examine some small sample properties related to these estimaters by some simulations.

• Journal of the Korean Data and Information Science Society
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• v.14 no.1
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• pp.1-9
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• 2003

In this paper we discuss Bayesian computation and model selection for Littlewood-Verrall model using Gibbs sampling. A numerical example with a simulated data is given.

• The KIPS Transactions:PartD
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• v.9D no.3
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• pp.389-398
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• 2002

Software reliability growth models are used in testing stages of software development to model the error content and time intervals between software failures. This paper presents a stochastic model for the software failure phenomenon based on a nonhomogeneous Poisson process(NHPP) and performs Bayesian inference using prior information. The failure process is analyzed to develop a suitable mean value function for the NHPP ; expressions are given for several performance measure. Actual software failure data are compared with several model on the constant reflecting the quality of testing. The performance measures and parametric inferences of the suggested models using Rayleigh distribution and Laplace distribution are discussed. The results of the suggested models are applied to real software failure data and compared with Goel model. Tools of parameter point inference and 95% credible intereval was used method of Gibbs sampling. In this paper, model selection using the sum of the squared errors was employed. The numerical example by NTDS data was illustrated.

• Communications for Statistical Applications and Methods
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• v.4 no.3
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• pp.753-763
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• 1997

컴퓨터의 발전에 따른 MCMC를 비동질적 포아송 과정에 이용하였다. 베이지안 추론에서 조건부 분포를 가지고 사후분포를 결정하는데 있어서의 계산 문제를 고려하였다. 특히 분포가 이중지수, 곰페르츠, 랄리, 감마, 그리고 검벨인 일반 순서통계량 모형에 대하여 깁스 샘플링과 메트로폴리스 알고리즘을 활용한 베이지안 계산과 모형선택을 제시하였다.