• Communications for Statistical Applications and Methods
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• v.4 no.2
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• pp.465-471
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• 1997

This paper deals with the problems of obtaining some Bayesian and empirical Bayesian Predictive densities and prediction intervals of a future observation $X_{(\tau+\gamma)}$ in the Rayleigh distribution. Using an inverse gamma prior distribution, some prodictive densities and prodiction intervals are proposed and studied. Also the behaviors of the proposed results are examined via numerical examples.

• The Korean Journal of Applied Statistics
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• v.27 no.6
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• pp.1069-1076
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• 2014

Rainfall weather patterns have changed due to global warming and sudden heavy rainfalls have become more frequent. Economic loss due to heavy rainfall has increased. We study the generalized Pareto distribution for modelling rainfall in Seoul based on data from 1973 to 2008. We use several priors including Jeffrey's noninformative prior and Gibbs sampling method to derive Bayesian posterior predictive distributions. The probability of heavy rainfall has increased over the last ten years based on estimated posterior predictive distribution.

• Communications for Statistical Applications and Methods
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• v.10 no.2
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• pp.268-275
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• 2003

We consider the Bayesian accelerated failure time model. The error distribution is assigned a skewed normal distribution which is including normal distribution. For noninformative priors of regression coefficients, we show the propriety of posterior distribution. A Markov Chain Monte Carlo algorithm(i.e., Gibbs Sampler) is used to obtain a predictive distribution for a future observation and Bayes estimates of regression coefficients.

• Communications for Statistical Applications and Methods
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• v.24 no.6
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• pp.561-581
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• 2017

Bayesian statistics can play a key role in the design and analysis of clinical trials and this has been demonstrated for medical device trials. By 1995 Bayesian statistics had been well developed and the revolution in computing powers and Markov chain Monte Carlo development made calculation of posterior distributions within computational reach. The Food and Drug Administration (FDA) initiative of Bayesian statistics in medical device clinical trials, which began almost 20 years ago, is reviewed in detail along with some of the key decisions that were made along the way. Both Bayesian hierarchical modeling using data from previous studies and Bayesian adaptive designs, usually with a non-informative prior, are discussed. The leveraging of prior study data has been accomplished through Bayesian hierarchical modeling. An enormous advantage of Bayesian adaptive designs is achieved when it is accompanied by modeling of the primary endpoint to produce the predictive posterior distribution. Simulations are crucial to providing the operating characteristics of the Bayesian design, especially for a complex adaptive design. The 2010 FDA Bayesian guidance for medical device trials addressed both approaches as well as exchangeability, Type I error, and sample size. Treatment response adaptive randomization using the famous extracorporeal membrane oxygenation example is discussed. An interesting real example of a Bayesian analysis using a failed trial with an interesting subgroup as prior information is presented. The implications of the likelihood principle are considered. A recent exciting area using Bayesian hierarchical modeling has been the pediatric extrapolation using adult data in clinical trials. Historical control information from previous trials is an underused area that lends itself easily to Bayesian methods. The future including recent trends, decision theoretic trials, Bayesian benefit-risk, virtual patients, and the appalling lack of penetration of Bayesian clinical trials in the medical literature are discussed.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.28 no.3
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• pp.26-35
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• 2005

This paper is intended to compare the hazard rate estimations from Bayesian approach and maximum likelihood estimate(MLE) method. Hazard rate frequently involves unknown parameters and it is common that those parameters are estimated from observed data by using MLE method. Such estimated parameters are appropriate as long as there are sufficient data. Due to various reasons, however, we frequently cannot obtain sufficient data so that the result of MLE method may be unreliable. In order to resolve such a problem we need to rely on the judgement about the unknown parameters. We do this by adopting the Bayesian approach. The first one is to use a predictive distribution and the second one is a method called Bayesian estimate. In addition, in the Bayesian approach, the prior distribution has a critical effect on the result of analysis, so we introduce the method using computerized-simulation to elicit an effective prior distribution. For the simplicity, we use exponential and gamma distributions as a likelihood distribution and its natural conjugate prior distribution, respectively. Finally, numerical examples are given to illustrate the potential benefits of the Bayesian approach.

• Journal of the Korean Data and Information Science Society
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• v.8 no.1
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• pp.21-30
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• 1997

In accelerated life tests, the failure time of an item is observed under a high stress level, and based on the time the performances of items are investigated at the normal stress level. In this paper, when the mean of the prior of a failure rate is known in the exponential lifetime distribution with censored accelerated failure time data, we utilize the empirical Bayesian method by using the moment estimators in order to estimate the parameters of the prior distribution and obtain the empirical Bayesian predictive density and predictive intervals for a future observation under the normal stress level.

• Computational Structural Engineering : An International Journal
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• v.1 no.2
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• pp.81-87
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• 2001

A framework for reliability analysis of structural components and systems under conditions of statistical and model uncertainty is presented. The Bayesian parameter estimation method is used to derive the posterior distribution of model parameters reflecting epistemic uncertainties. Point, predictive and bound estimates of reliability accounting for parameter uncertainties are derived. The bounds estimates explicitly reflect the effect of epistemic uncertainties on the reliability measure. These developments are enhance-ments of second-moment uncertainty analysis methods developed by A. H-S. Ang and others three decades ago.

• Journal of the Korean Data and Information Science Society
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• v.13 no.1
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• pp.139-145
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• 2002

This paper deals with the problem of obtaining the Bayesian predictive density function and the prediction intervals for a future observation and the p-th order statistics of n future observations for the exponential model under the censored sampling with incomplete information.

• Communications for Statistical Applications and Methods
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• v.13 no.1
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• pp.177-190
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• 2006

The aim of this study is to propose a Bayesian model for fitting mortality rate of colon cancer. For the analysis of mortality rate of a disease, factors such as age classes of population and spatial characteristics of the location are very important. The model proposed in this study allows the age class to be a random effect in addition to its conventional role as the covariate of a linear regression, while the spatial factor being a random effect. The model is fitted using Metropolis-Hastings algorithm. Posterior expected predictive deviances, standardized residuals, and residual plots are used for comparison of models. It is found that the proposed model has smaller residuals and better predictive accuracy. Lastly, we described patterns in disease maps for colon cancer.

• Journal of Korean Institute of Industrial Engineers
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• v.16 no.2
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• pp.135-147
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• 1990

A nuclear power plant can be viewed as a large complex man-machine system where high system reliability is obtained by ensuring that sub-systems are designed to operate at a very high level of performance. The chance of severe accident involving at least partial core-melt is very low but once it happens the consequence is very catastrophic. The prediction of risk in low probability, high-risk incidents must be examined in the contest of general engineering knowledge and operational experience. Engineering knowledge forms part of the prior information that must be quantified and then updated by statistical evidence gathered from operational experience. Recently, Bayesian procedures have been used to estimate rate of accident and to predict future risks. The Bayesian procedure has advantages in that it efficiently incorporates experts opinions and, if properly applied, it adaptively updates the model parameters such as the rate or probability of accidents. But at the same time it has the disadvantages of computational complexity. The predictive distribution for the time to next incident can not always be expected to end up with a nice closed form even with conjugate priors. Thus we often encounter a numerical integration problem with high dimensions to obtain a predictive distribution, which is practically unsolvable for a model that involves many parameters. In order to circumvent this difficulty, we propose a method of approximation that essentially breaks down a problem involving many integrations into several repetitive steps so that each step involves only a small number of integrations.