• Journal of the Korean Statistical Society
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• 제26권4호
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• pp.477-491
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• 1997

A new predictive classification rule for assigning future cases into one of two multivariate normal population (with unknown normal mixture model) is considered. The development involves calculation of posterior probability of each possible normal-mixture model via a default Bayesian test criterion, called intrinsic Bayes factor, and suggests predictive distribution for future cases to be classified that accounts for model uncertainty by weighting the effect of each model by its posterior probabiliy. In this paper, our interest is focused on constructing the classification rule that takes care of uncertainty about the types of covariance matrices (homogeneity/heterogeneity) involved in the model. For the constructed rule, a Monte Carlo simulation study demonstrates routine application and notes benefits over traditional predictive calssification rule by Geisser (1982).

• Journal of the Korean Data and Information Science Society
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• 제24권6호
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• pp.1455-1464
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• 2013

This paper develops maximum likelihood estimators (MLEs) of unknown parameters in an exponentiated half-logistic distribution based on a progressively type-II censored sample. We obtain approximate confidence intervals for the MLEs by using asymptotic variance and covariance matrices. Using importance sampling, we obtain Bayes estimators and corresponding credible intervals with the highest posterior density and Bayes predictive intervals for unknown parameters based on progressively type-II censored data from an exponentiated half logistic distribution. For illustration purposes, we examine the validity of the proposed estimation method by using real and simulated data.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회 1993년도 추계학술대회발표논문집; 서강대학교, 서울; 25 Sep. 1993
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• pp.24-30
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• 1993

When modeling a complex system we use an event tree to analyze propagation of failure. An event tree cannot represent the statistical interrelationships among parameters, but it can be represented as a statistically identical influence diagram so that parameter updating can be easily performed. After updating parameters we can calculate posterior distribution of the failure rate for each path. But exact distribution requires considerably complex numerical integration. We propose an approximation method to calculate the posterior and derive the predictive distribution of the time to next failure. Finally we introduce the system which implements our methodology.

• Journal of the Korean Statistical Society
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• 제30권2호
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• pp.179-192
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• 2001

When a statistical model has a hierarchical structure such as multilayer perceptrons in neural networks or Gaussian mixture density representation, the model includes distribution with unidentifiable parameters when the structure becomes redundant. Since the exact structure is unknown, we need to carry out statistical estimation or learning of parameters in such a model. From the geometrical point of view, distributions specified by unidentifiable parameters become a singular point in the parameter space. The problem has been remarked in many statistical models, and strange behaviors of the likelihood ratio statistics, when the null hypothesis is at a singular point, have been analyzed so far. The present paper studies asymptotic behaviors of the maximum likelihood estimator and the Bayesian predictive estimator, by using a simple cone model, and show that they are completely different from regular statistical models where the Cramer-Rao paradigm holds. At singularities, the Fisher information metric degenerates, implying that the cramer-Rao paradigm does no more hold, and that he classical model selection theory such as AIC and MDL cannot be applied. This paper is a first step to establish a new theory for analyzing the accuracy of estimation or learning at around singularities.

• 대한산업공학회지
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• 제26권3호
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• pp.193-199
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• 2000

In many studies, considerable attention has been focussed upon choosing a model which represents underlying process of time series and forecasting the future. In the real world, however, there may be some cases that one model can not reflect all the characteristics of original time series. Under such circumstances, we may get better performance by combining the forecasts from several models. The most popular methods for combining forecasts involve taking a weighted average of multiple forecasts. But the weights are usually unstable. In cases the assumptions of normality and unbiasedness for forecast errors are satisfied, a Bayesian method can be used for updating the weights. In the real world, however, there are many circumstances the Bayesian method is not appropriate. This paper proposes a PNN(Probabilistic Neural Net) approach as a method for combining forecasts that can be applied when the assumption of normality or unbiasedness for forecast errors is not satisfied. In this paper, PNN method, which is similar to Bayesian approach, is suggested as an updating method of the unstable weights in the combination of the forecasts. The PNN method has been usually used in the field of pattern recognition. Unlike the Bayesian approach, it requires no assumption of a specific prior distribution because it gets probabilities by using the distribution estimated from given data. Empirical results reveal that the PNN method offers superior predictive capabilities.

• 응용통계연구
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• 제21권5호
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• pp.835-843
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• 2008

In this paper, we investigate a Bayesian inference for software reliability models based on mean value functions which take the form of the mixture of beta distribution functions. The posterior simulation via the Markov chain Monte Carlo approach is used to produce estimates of posterior properties. Its applicability is illustrated with two real data sets. We compute the predictive distribution and the marginal likelihood of various models to compare the performance of them. The model comparison results show that the model based on the beta-mixture performs better than other models.

• 대한기계학회논문집A
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• 제35권4호
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• pp.393-400
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• 2011

본 연구에서는 현장의 축적된 피로 수명 시험 데이터를 바탕으로 유한요소해석(Finite Element Analysis)을 이용하여 스프링의 피로 수명 파라미터를 역 추정(Inverse Estimation)하는 연구를 수행하였다. 베이지안 접근법(Bayesian Approach)을 이용하여 불확실성 피로 수명 파라미터의 사후분포(Posterior distribution)를 구하였고, 마코프체인몬테카를로(Markov Chain Monte Carlo) 기법을 이용하여 역 추정된 파라미터의 샘플 데이터를 생성하였다. 얻어진 샘플링 데이터를 기반으로 피로 수명을 예측한 결과 신뢰 수준 내에서 실제 수명 시험 결과가 예측한 범위 내에 잘 포함되고 있음을 알 수 있었다.

• 한국콘텐츠학회논문지
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• 제21권11호
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• pp.77-86
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• 2021

시간적인 차이를 두고 획득한 이질적인 과거 전쟁 결과 데이터를 하나의 모형으로 구축하는 방법으로 베이지안 추론에 의한 전쟁시뮬레이션 모형을 구축하는 방법을 제안하였다. 과거의 전쟁 결과를 분석하여 미래에 있을 수 있는 전쟁을 예측하는 방법으로 선형회귀모형을 적용하는 방법을 고려할 수 있다. 그러나 역사적으로 시대가 서로 달라 전장 환경의 변화가 반영된 이질적인 두 유형의 자료들이라면 모형의 가정사항 위반으로 하나의 선형회귀모형으로 적합하는 것은 적절하지 않다. 이러한 문제를 해결하기 위해 앞선 시대에 있는 자료를 비정보적 사전분포로 가정하여 사후분포를 구하고 이를 다음 시대에 얻은 자료를 분석하기 위한 사전분포로 활용하여 최종 사후분포를 추론하는 베이지안 추론 방법을 제안하였다. 베이지안 추론 방법의 또 다른 장점은 마코프 체인 몬테 카를로 방법으로 샘플링한 결과를 이용하여 불확실성이 반영된 사후분포나 사후예측분포를 추론할 수 있다는 점이다. 이렇게 했을 때 고전적인 선형회귀모형으로 분석하는 것보다 다양한 정보를 활용할 수 있을 뿐만 아니라 향후 추가적으로 획득되는 자료도 모형에 반영하여 모형을 계속 업데이트시킬 수 있다는 장점이 있다.

• Journal of the Korean Statistical Society
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• 제25권4호
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• pp.577-588
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• 1996

The Bayes factor provides a possible hierarchical Bayesian approach for studying the change point problems. A hypothesis for testing change versus no change is considered using predictive distributions. When the underlying distribution is in one-parameter exponential family with conjugate priors, Bayes factors are investigated to the hypothesis above. Finally one example is provided .

• 한국수자원학회논문집
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• 제53권7호
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• pp.481-491
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• 2020

새만금 농업단지가 조성됨에 따라 농업용수 공급이 요구되며, 농업적 측면에서 염분은 작물 재배시 생육에 영향을 미치는 항목으로 농업용수 공급시 철저한 관리가 요구된다. 따라서 농작물에 영향을 미치지 않는 농업용수 공급을 위해 염분계측을 통한 체계적인 농업용수 관리가 필요하다. 본 연구에서는 새만금호내에 관측되는 염분 시계열 자료를 모의하기 위해서 자기회귀모형을 기반으로 한 Two-Stage ARX 모형을 개발하였다. 층별로 나눠진 염분자료를 계층적 Bayesian기법을 활용하여 매개변수를 확률분포형으로 추정하였으며 염분모의의 불확실성을 제시하였다. 최적 모형을 선정하기 위해서 통계적 지표인 BIC값을 이용하였으며, 최종적으로 선정된 모형을 통해 양수장 인근 수역의 염분 모의 결과를 제시하였다.