• 한국수학사학회지
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• 제11권1호
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• pp.68-77
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• 1998

There are two approach methods widely in statistical inferences. First is sampling theory methods and the other is Bayesian methods. In this paper, we will introduce the most basic differences of the two approach methods. Especially, we investigate and introduce the historical origin of Bayesian methods in Statistical inferences which is currently used. Also, we introduce the some characteristics of sampling theory method and Bayesian methods.

• Journal of Radiation Protection and Research
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• 제41권2호
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• pp.149-154
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• 2016

Background: Any real application of Bayesian inference must acknowledge that both prior distribution and likelihood function have only been specified as more or less convenient approximations to whatever the analyzer's true belief might be. If the inferences from the Bayesian analysis are to be trusted, it is important to determine that they are robust to such variations of prior and likelihood as might also be consistent with the analyzer's stated beliefs. Materials and Methods: The robust Bayesian inference was applied to atmospheric dispersion assessment using Gaussian plume model. The scopes of contaminations were specified as the uncertainties of distribution type and parametric variability. The probabilistic distribution of model parameters was assumed to be contaminated as the symmetric unimodal and unimodal distributions. The distribution of the sector-averaged relative concentrations was then calculated by applying the contaminated priors to the model parameters. Results and Discussion: The sector-averaged concentrations for stability class were compared by applying the symmetric unimodal and unimodal priors, respectively, as the contaminated one based on the class of ${\varepsilon}$-contamination. Though ${\varepsilon}$ was assumed as 10%, the medians reflecting the symmetric unimodal priors were nearly approximated within 10% compared with ones reflecting the plausible ones. However, the medians reflecting the unimodal priors were approximated within 20% for a few downwind distances compared with ones reflecting the plausible ones. Conclusion: The robustness has been answered by estimating how the results of the Bayesian inferences are robust to reasonable variations of the plausible priors. From these robust inferences, it is reasonable to apply the symmetric unimodal priors for analyzing the robustness of the Bayesian inferences.

• 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.

• Nuclear Engineering and Technology
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• 제53권2호
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• pp.357-367
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• 2021

In general, common cause failures (CCFs) have been modeled with the assumption that components within the same group are symmetric. This assumption reduces the number of parameters required for the CCF probability estimation and allows us to use a parametric model, such as the alpha factor model. Although there are various asymmetric conditions in nuclear power plants (NPPs) to be addressed, the traditional CCF models are limited to symmetric conditions. Therefore, this paper proposes the copulabased CCF model to deal with asymmetric as well as symmetric CCFs. Once a joint distribution between the components is constructed using copulas, the proposed model is able to provide the probability of common cause basic events (CCBEs) by formulating a system of equations without symmetry assumptions. In addition, Bayesian inferences for the parameters of the marginal and copula distributions are introduced and Markov Chain Monte Carlo (MCMC) algorithms are employed to sample from the posterior distribution. Three example cases using simulated data, including asymmetry conditions in total failure probabilities and/or dependencies, are illustrated. Consequently, the copula-based CCF model provides appropriate estimates of CCFs for asymmetric conditions. This paper also discusses the limitations and notes on the proposed method.

• Communications for Statistical Applications and Methods
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• 제3권2호
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• pp.161-168
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• 1996

Multistage hierarchical models and Bayesian inferences about finite population total estimations are considered. Here, Gibbs sampling approach that can be used to predict the marginal posterior means needed for Bayesian inferences is proposed.

• Journal of the Korean Data and Information Science Society
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• 제17권3호
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• pp.843-850
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• 2006

In this paper, we consider the Bayesian multiple comparisons problem for K bivariate exponential populations to make inferences on the relationships among the parameters based on observations. And we suggest the Bayesian procedure based on fractional Bayes factor when noninformative priors are applied for the parameters. Also, we give a numerical examples to illustrate our procedure.

• 한국수학사학회지
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• 제13권1호
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• pp.99-112
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• 2000

In this paper we discuss the teaching methods about statistical inferences. Bayesian methods have the attractive feature that statistical conclusions can be stated using the language of subjective probability. Simple methods of teaching Bayes' rule described, and these methods are illustrated for inference and prediction problems for one proportions. Also, we discuss the advantages and disadvantages of traditional and Bayesian approachs in teaching inference.

• 논리연구
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• 제8권1호
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• pp.47-67
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• 2005

베이즈망은 탐구 공간을 구성하는 변수들 사이에 성립하는 확률적 관계를 이용하여 그 변수들 사이에 성립된다고 가정되는 인과 관계를 추론하는데 이용된다. 베이즈망에 관한 철학적 논쟁의 대상은 특정한 변수들의 확률적 독립성을 가정하는 인과적 마코프 조건이다. 베이즈망 이론에 대한 강력한 비판자인 카트라이트는 인과적 마코프 조건이 비결정적 세계에서는 성립될 수 없기 때문에 인과적 추리에 대한 타당한 원리가 될 수 없다고 주장한다. 이글의 목적은 인과적 마코프 조건이 인과적 추리에 대한 타당한 원리가 될 수 없다는 카트라이트의 비판이 타당한가를 검토하는 것이다. 나는 인과적 사건들의 연쇄를 허용하는 연속모델은 카트라이트의 비판을 벗어날 수 있다고 주장한다.

• Communications for Statistical Applications and Methods
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• 제14권1호
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• pp.121-131
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• 2007

In this paper, we examine the problem of estimating the sensitive characteristics and behaviors in a multinomial randomized response model using Bayesian approach. We derived a posterior distribution for parameter of interest for multinomial randomized response model. Based on the posterior distribution, we also calculated a credible intervals and mean squared error (MSE). We finally compare the maximum likelihood estimator and the Bayes estimator in terms of MSE.

• Communications for Statistical Applications and Methods
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• 제21권2호
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• pp.135-145
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• 2014

The present study surveys Bayesian modeling structure for inferences about transition probabilities of Markov chain. The motivation of the study came from the data that shows transitional behaviors of emotionally disturbed children undergoing residential treatment program. Dirichlet distribution was used as prior for the multinomial distribution. The analysis with real data was implemented in WinBUGS programming environment. The performance of the model was compared to that of alternative approaches.