• Journal of the Korean Statistical Society
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• v.28 no.4
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• pp.443-455
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• 1999

A simulation-based approach to estimating the probability of an arbitrary region under a multivariate normal distribution is developed. In specific, the probability is expressed as the ratio of the unrestricted and the restricted multivariate normal density functions, where the restriction is given by the region whose probability is of interest. The density function of the restricted distribution is then estimated by using a sample generated from the Gibbs sampling algorithm.

• Communications for Statistical Applications and Methods
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• v.14 no.2
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• pp.345-353
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• 2007

A Bayesian estimation of the Nakagami-m fading parameter is developed. Bayesian estimation is performed by Gibbs sampling, including adaptive rejection sampling. A Monte Carlo study shows that the Bayesian estimators proposed outperform any other estimators reported elsewhere in the sense of bias, variance, and root mean squared error.

• Communications for Statistical Applications and Methods
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• v.8 no.2
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• pp.417-426
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• 2001

This paper addresses the nonparametric Bayesian estimation for the exponential populations under type II censoring. The Dirichlet process prior is used to provide nonparametric Bayesian estimates of parameters of exponential populations. In the past, there have been computational difficulties with nonparametric Bayesian problems. This paper solves these difficulties by a Gibbs sampler algorithm. This procedure is applied to a real example and is compared with a classical estimator.

• Communications for Statistical Applications and Methods
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• v.8 no.2
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• pp.427-434
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• 2001

In this paper, we consider the nonparametric Bayesian approach to the multiple comparisons problem for I Poisson populations using Dirichlet process priors. We describe Gibbs sampling algorithm for calculating posterior probabilities for the hypotheses and calculate posterior probabilities for the hypotheses using Markov chain Monte Carlo. Also we provide a numerical example to illustrate the developed numerical technique.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.269-274
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• 2004

We investigate a deranged Cantor set (a generalized Cantor set) using the similar method to find the dimensions of cookie-cutter repeller. That is, we will use a Gibbs measure which is a weak limit of a subsequence of discrete Borel measures to find the dimensions. The deranged Cantor set that will be considered is a generalized form of a perturbed Cantor set (a variation of the symmetric Cantor set) and a cookie-cutter repeller.

• Journal of the Korean Data and Information Science Society
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• v.11 no.1
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• pp.127-137
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• 2000

In this paper, we consider hierarchical Bayesian analysis for P(Y < X) using Gibbs sampler, where X and Y are independent normal distributions with unknown means and variances, respectively. Also numerical study using real data is provided.

• Journal of the Korean Mathematical Society
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• v.37 no.4
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• pp.579-592
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• 2000

We study the variational principle for quantum unbounded spin systems interacting via superstable and regular interactions. We show that the (weak) KMS state constructed via the thermodynamic limit of finite volume Green's functions satisfies the Gibbs variational equality.

• Communications for Statistical Applications and Methods
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• v.7 no.1
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• pp.165-178
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• 2000

Bayesian methods are considered for the multiple caputure-recapture data. Reference priors are developed for such model and sampling-based approach through Gibbs sampler is used for inference from posterior distributions. Furthermore approximate Bayes factors are obtained for model selection between trap and nontrap response models. Finally one methodology is implemented for a capture-recapture model in generated data and real data.

• Journal of the Korean Statistical Society
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• v.36 no.1
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• pp.77-91
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• 2007

This paper considers development of noninformative priors for the familial data when the families have equal number of offspring. Several noninformative priors including the widely used Jeffreys' prior as well as the different reference priors are derived. Also, a simultaneously-marginally-probability-matching prior is considered and probability matching priors are derived when the parameter of interest is inter- or intra-class correlation coefficient. The simulation study implemented by Gibbs sampler shows that two-group reference prior is slightly edge over the others in terms of coverage probability.

• Journal of the Korean Statistical Society
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• v.31 no.1
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• pp.93-107
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• 2002

Random effects generalised linear models are useful for analysing clustered count data in which responses are usually correlated. We propose a Bayesian approach to parameter estimation and variable selection in random effects generalised linear models for count data. A simple Gibbs sampling algorithm for parameter estimation is presented and a simple and efficient variable selection is done by using the Gibbs outputs. An illustrative example is provided.