• Communications for Statistical Applications and Methods
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• 제12권3호
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• pp.729-742
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• 2005

In this paper, we discuss the propriety of the various noninformative priors for the Pareto distribution. The reference prior, Jeffreys prior and ad hoc noninformative prior which is used in several literatures will be introduced and showed that which prior gives the proper posterior distribution. The reference prior and Jeffreys prior give a proper posterior distribution, but ad hoc noninformative prior which is proportional to reciprocal of the parameters does not give a proper posterior. To compute survival function, we use the well-known approximation method proposed by Lindley (1980) and Tireney and Kadane (1986). And two methods are compared by simulation. A real data example is given to illustrate our methodology.

• Communications for Statistical Applications and Methods
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• 제10권1호
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• pp.1-9
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• 2003

In this article, we consider a Bayesian estimation method for the geometric mean of $textsc{k}$ exponential parameters, Using the Tibshirani's orthogonal parameterization, we suggest an invariant prior distribution of the $textsc{k}$ parameters. It is seen that the prior, probability matching prior, is better than the uniform prior in the sense of correct frequentist coverage probability of the posterior quantile. Then a weighted Monte Carlo method is developed to approximate the posterior distribution of the mean. The method is easily implemented and provides posterior mean and HPD(Highest Posterior Density) interval for the geometric mean. A simulation study is given to illustrates the efficiency of the method.

• Communications for Statistical Applications and Methods
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• 제12권2호
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• pp.395-411
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• 2005

In this paper, we develop the Jeffreys' prior, reference prior and the the probability matching priors for the difference of intraclass correlation coefficients in familial data. e prove the sufficient condition for propriety of posterior distributions. Using marginal posterior distributions under those noninformative priors, we compare posterior quantiles and frequentist coverage probability.

• 한국신뢰성학회지:신뢰성응용연구
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• 제17권3호
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• pp.188-196
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• 2017

Purpose: The purpose of this research is to determine optimal replacement age using non-informative prior information and Bayesian method. Methods: We propose a novel approach using Bayesian method to determine the optimal replacement age in block replacement policy by defining the prior probability with data on failure time and repair time. The Marcov Chain Monte Carlo simulation is used to investigate the asymptotic distribution of posterior parameters. Results: An optimal replacement age of block replacement policy is determined which minimizes cost and nonoperating time when no information on prior distribution of parameters is given. Conclusion: We find the posterior distribution of parameters when lack of information on prior distribution, so that the optimal replacement age which minimizes the total cost and maximizes the total values is determined.

• Communications for Statistical Applications and Methods
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• 제3권3호
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• pp.215-223
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• 1996

By using Tukey's generalized lambda distribution, appoximate posterior density is derived under the Bayes-empirical Bayes model. The sensitivity of posterior distribution to the hyperprior distribution is examined by using Tukey's generalized lambda distriburion which approximate many well-knmown distributions. Based upon Monte Varlo simulation studies it can be said that posterior distribution is sensitive to the cariance of the prior distribution and to the symmetry of the hyperprior distribution. Also posterior distribution is approximately obtained by using the following methods : Lindley method, Laplace method and Gibbs sampler method.

• 한국안전학회지
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• 제36권2호
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• pp.32-38
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• 2021

This paper suggests an approach to evaluate the reliability of an intelligent power module with information deficiency of prior distribution and the characteristics of censored data through Bayesian statistics. This approach used a prior distribution of Bayesian statistics using the lifetime information provided by the manufacturer and compared and evaluated diffuse prior (vague prior) distributions. To overcome the computational complexity of Bayesian posterior distribution, it was computed with Gibbs sampling in the Monte Carlo simulation method. As a result, the standard deviation of the prior distribution developed using simple information was smaller than that of the posterior distribution calculated with the diffuse prior. In addition, it showed excellent error characteristics on RMSE compared with the Kaplan-Meier method.

• Communications for Statistical Applications and Methods
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• 제11권1호
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• pp.161-168
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• 2004

A single-index model is useful in fields which employ multidimensional regression models. Many methods have been developed in parametric and nonparametric approaches. In this paper, posterior inference is considered and a wavelet series is thought of as a function approximated to a true function in the single-index model. The posterior inference needs a prior distribution for each parameter estimated. A prior distribution of each coefficient of the wavelet series is proposed as a hierarchical distribution. A direction $\beta$ is assumed with a unit vector and affects estimate of the true function. Because of the constraint of the direction, a transformation, a spherical polar coordinate $\theta$, of the direction is required. Since the posterior distribution of the direction is unknown, we apply a Metropolis-Hastings algorithm to generate random samples of the direction. Through a Monte Carlo simulation we investigate estimates of the true function and the direction.

• Journal of the Korean Data and Information Science Society
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• 제22권6호
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• pp.1183-1197
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• 2011

베이즈 법칙에서는 사전확률과 우도가 주어지고 어떤 실험결과가 일어났을 때 사후확률을 계산한다. 이러한 사후확률의 계산 문제를 엑셀 매크로를 이용하여 쉽게 계산할 수 있다. 또한 일련의 독립적이고 연속적인 실험결과에 따르는 사후확률도 편리하게 계산할 수 있다. 특히, 엑셀 매크로를 작성하면 작업창에서 반복된 계산의 입력과 출력이 쉽게 이루어진다. 본 논문에서는 베이즈 법칙의 활용을 위해서 엑셀 매크로를 작성하고 그것의 사용 예를 들었다.

• Communications for Statistical Applications and Methods
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• 제9권1호
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• pp.221-227
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• 2002

The concept of pivot has been widely used in various classical inferences. In this paper, it is proved by use of pivotal quantities that the Bayesian inferences can be arrived at the same results of classical inferences for the location-scale parameters models under the assumption of non-informative prior distributions. Some theorems are proposed in which the posterior distribution and the sampling distribution of a pivotal quantity coincide. The theorems are applied illustratively to some statistical models.

• International Journal of Reliability and Applications
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• 제2권2호
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• pp.117-130
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• 2001

Consider the problem of estimating the system reliability using noninformative priors when both stress and strength follow generalized gamma distributions. We first treat the orthogonal reparametrization and then, using this reparametrization, derive Jeffreys'prior, reference prior, and matching priors. We next provide the suffcient condition for propriety of posterior distributions under those noninformative priors. Finally, we provide and compare estimated values of the system reliability based on the simulated values of the parameter of interest in some special cases.