• Journal of the Korean Statistical Society
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• v.36 no.2
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• pp.321-333
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• 2007

In the proportional hazard model with the beta process prior, the posterior computation with the discrete approximation is considered. The time period of interest is partitioned by small intervals. On each partitioning interval, the likelihood is approximated by that of a binomial experiment and the beta process prior is by a beta distribution. Consequently, the posterior is approximated by that of many independent binomial model with beta priors. The analysis of the leukemia remission data is given as an example. It is illustrated that the length of the partitioning interval affects the posterior and one needs to be careful in choosing it.

• Communications for Statistical Applications and Methods
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• v.27 no.4
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• pp.413-430
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• 2020

The multiply Type-II hybrid censoring scheme is disadvantaged by an experiment time that is too long. To overcome this limitation, we propose a generalized multiply Type-II hybrid censoring scheme. Some estimators of the scale parameter of the exponential distribution are derived under a generalized multiply Type-II hybrid censoring scheme. First, the maximum likelihood estimator of the scale parameter of the exponential distribution is obtained under the proposed censoring scheme. Second, we obtain the Bayes estimators under different loss functions with a noninformative prior and an informative prior. We approximate the Bayes estimators by Lindleys approximation and the Tierney-Kadane method since the posterior distributions obtained by the two priors are complicated. In addition, the Bayes estimators are obtained by using the Markov Chain Monte Carlo samples. Finally, all proposed estimators are compared in the sense of the mean squared error through the Monte Carlo simulation and applied to real data.

• Journal of the Korean Data and Information Science Society
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• v.22 no.1
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• pp.115-123
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• 2011

In this paper, we develop the noninformative priors for stress-strength reliability from the Pareto distributions. We develop the matching priors and the reference priors. It turns out that the second order matching prior does not match the alternative coverage probabilities, and is not a highest posterior density matching or a cumelative distribution function matching priors. Also we reveal that the one-at-a-time reference prior and Jeffreys' prior are the second order matching prior. We show that the proposed reference prior matches the target coverage probabilities in a frequentist sense through simulation study, and an example is given.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.09b
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• pp.45-48
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• 2003

We propose some properties of Bayesian fuzzy hypotheses testing by revision for prior possibility distribution and posterior possibility distribution using weighted fuzzy hypotheses H$\sub$0/($\theta$) versus H$_1$($\theta$) on $\theta$ with loss function.

• Magazine of the Korea Concrete Institute
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• v.11 no.2
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• pp.241-249
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• 1999

To estimate the compressive strength of concrete more realistically, relative large number of data are necessary. However, it is very common in practice that only limited data are available. The purpose of the present paper is therefore to propose a realistic method to estimate the compressive strength of concrete with limited data in actual site. The Bayesian method of statistical analysis has been applied to the problem of the estimation of compressive strength of concrete. The mean compressive strength is considered as the random parameter and a prior distribution is selected to enable updating of the Bayesian distribution of compressive strength of concrete reflecting both existing data and sampling observations. The updating of the Bayesian distribution with increasing data is illustrated in numerical application. It is shown that by combining prior estimation with information from site observation, more precise estimation is possible with relatively small sampling. It is also seen that the contribution of the prior in determining the posterior distribution depends on its sharpness or flatness in relation to the sharpness or flatness of the likelihood function. The present paper allows more realistic determination of concrete strength in site with limited data.

• Journal of Communications and Networks
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• v.7 no.4
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• pp.438-449
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• 2005

In this paper, we describes the information-theoretic approaches to sensor selection and sensor placement in sensor net­works for target localization and tracking. We have developed a sensor selection heuristic to activate the most informative candidate sensor for collaborative target localization and tracking. The fusion of the observation by the selected sensor with the prior target location distribution yields nearly the greatest reduction of the entropy of the expected posterior target location distribution. Our sensor selection heuristic is computationally less complex and thus more suitable to sensor networks with moderate computing power than the mutual information sensor selection criteria. We have also developed a method to compute the posterior target location distribution with the minimum entropy that could be achieved by the fusion of observations of the sensor network with a given deployment geometry. We have found that the covariance matrix of the posterior target location distribution with the minimum entropy is consistent with the Cramer-Rao lower bound (CRB) of the target location estimate. Using the minimum entropy of the posterior target location distribution, we have characterized the effect of the sensor placement geometry on the localization accuracy.

• Communications for Statistical Applications and Methods
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• v.29 no.4
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• pp.471-486
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• 2022

Autoregressive moving average (ARMA) models involve nonlinearity in the model coefficients because of unobserved lagged errors, which complicates the likelihood function and makes the posterior density analytically intractable. In order to overcome this problem of posterior analysis, some approximation methods have been proposed in literature. In this paper we first review the main analytic approximations proposed to approximate the posterior density of ARMA models to be analytically tractable, which include Newbold, Zellner-Reynolds, and Broemeling-Shaarawy approximations. We then use the Kullback-Leibler divergence to study the relation between these three analytic approximations and to measure the distance between their derived approximate posteriors for ARMA models. In addition, we evaluate the impact of the approximate posteriors distance in Bayesian estimates of mean and precision of the model coefficients by generating a large number of Monte Carlo simulations from the approximate posteriors. Simulation study results show that the approximate posteriors of Newbold and Zellner-Reynolds are very close to each other, and their estimates have higher precision compared to those of Broemeling-Shaarawy approximation. Same results are obtained from the application to real-world time series datasets.

• Journal of the Korean Statistical Society
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• v.31 no.4
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• pp.509-518
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• 2002

This paper is concerned with semiparametric Bayesian analysis of the proportional intensity regression model of the Poisson process for multiple event time data. A nonparametric prior distribution is put on the baseline cumulative intensity function and a usual parametric prior distribution is given to the regression parameter. Also we allow heterogeneity among the intensity processes in different subjects by using unobserved random frailty components. Gibbs sampling approach with the Metropolis-Hastings algorithm is used to explore the posterior distributions. Finally, the results are applied to a real data set.

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.1129-1140
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• 2005

A nonparametric Bayesian method for calculating posterior probabilities of the multiple comparison problem on the parameters of several Geometric populations is presented. Bayesian multiple comparisons under two different prior/ likelihood combinations was studied by Gopalan and Berry(1998) using Dirichlet process priors. In this paper, we followed the same approach to calculate posterior probabilities for various hypotheses in a statistical experiment with a partition on the parameter space induced by equality and inequality relationships on the parameters of several geometric populations. This also leads to a simple method for obtaining pairwise comparisons of probability of successes. Gibbs sampling technique was used to evaluate the posterior probabilities of all possible hypotheses that are analytically intractable. A numerical example is given to illustrate the procedure.

• Journal of the Korean Data and Information Science Society
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• v.21 no.6
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• pp.1327-1335
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• 2010

In this paper, we want to develop objective priors for the common location parameter in two half-t distributions with unequal scale parameters. The half-t distribution is a non-regular class of distribution. One can not develop the reference prior by using the algorithm of Berger of Bernardo (1989). Specially, we derive the reference priors and prove the propriety of joint posterior distribution under the developed priors. Through the simulation study, we show that the proposed reference prior matches the target coverage probabilities in a frequentist sense.