• Journal of the Korean Statistical Society
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• 제26권4호
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• pp.493-505
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• 1997

The analysis of binary data appears to many areas such as statistics, biometrics and econometrics. In many cases, data are often collected in which some observations are incomplete. Assume that the missing covariates are missing at random and the responses are completely observed. A method to Bayesian analysis of the binary regression model with incomplete data is presented. In particular, the desired marginal posterior moments of regression parameter are obtained using Meterpolis algorithm (Metropolis et al. 1953) within Gibbs sampler (Gelfand and Smith, 1990). Also, we compare logit model with probit model using Bayes factor which is approximated by importance sampling method. One example is presented.

• Journal of the Korean Data and Information Science Society
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• 제27권5호
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• pp.1423-1431
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• 2016

When the sample size in a certain domain is too small to produce adequate information, small area model with random effects is usually used. Also, if we do not consider an inherent pattern which data possess, it considerably affects inference. In this paper, we mainly focus on modeling to handle increased variation of the Current Population Survey (CPS) median income as the Internal Revenue Service (IRS) mean income increases. In a hierarchical Bayesian framework, most estimations are carried out through the Gibbs sampler while the grid method is used to generate parameters from non-standard form. Numerical study indicates that the performance of proposed model is better than that of CPS method in terms of four comparison measurements.

• 공학논문집
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• 제3권1호
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• pp.65-73
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• 1998

영상복원법 중에는 복원하고자 하는 원 영상의 화소밝기분포가 부분적으로 평탄하다는 가정을 한 부가적인 Gibbs 사전정보를 포함하는 방법이 있다. 이 경우 Gibbs 사전정보를 표현하기 위해 원 영상의 화소밝기를 나타내는 실변수 뿐 아니라 경계를 정의하는 이진변수를 포함하는 에너지 함수를 정의하게 된다. 그러나, 이러한 실변수와 이진변수의 복합형태가 존재할 경우 이들을 동시에 추정하는 것은 매우 어려운 것으로 알려져 있다. 본 연구에서는 deterministic annealing 방법의 응용을 고찰하기로 한다. Deterministic annealing 방법은 다른 방법과 달리 실수 값을 취하는 변수 및 이진변수가 복합형태로 존재하는 문제를 다루는데 있어서 매우 원리적이고 효율적인 방법을 제공한다. 이 방법에서는 복합형태를 취하는 원 함수에 근접하도록 하는 일련의 함수들을 정의하게 되는데, 이때 새로운 일련의 함수들은 실변수만을 취하도록 변환된다. 일련의 함수 중 개개의 함수는 조종파라미터(냉각시 온도에 해당)에 의해 지정된다. 고온에서의 에너지 함수는 저온에서의 에너지와 유사하나 좀더 완만한 형태를 취하게 된다. 따라서, 온도를 서서히 낮추면서 고온에서의 에너지 함수를 저온에서의 에너지 함수로 변환시켜 감으로써 에너지 함수를 최소화하는 작업이 용이해 진다. 이것이 연속방법의 핵심이다. 본 논문에서는 이러한 연속방법을 Bayesian 영상복원 모델에 적용하여 그 성능을 실험을 통해 검증한다.

• 응용통계연구
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• 제13권2호
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• pp.505-514
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• 2000

마코브체인 몬테칼로방법중에서 깁스 추출방법을 혼합 고장모형에 이용하였다. 베이자안 추론에서 조건부분포를 가지고 사후 분포를 결정하는데 있어서 계산 문제와 이론적인 정당성을 고려하여 감마족인 Rayleigh와 Erlang추세를 가진 혼합모형에 대하여 깁스샘플링 알고리즘을 이용하여 베이지안 계산과 신뢰도 추이를 알아보고 모의실험자료를 이용하여 수치적인 계산을 시행하고 그 결과를 제시하였다.

• Journal of the Korean Data and Information Science Society
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• 제7권2호
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• pp.247-256
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• 1996

본 논문은 깁스 표본 기법을 이용하여 Demster et al.(1981)에 의해 소개된 Field Mice자료를 분석하기 위하여 베이지안 계층적 모형을 적용시켜 보았다. Jeffrey의 사전확률을 이용한 사후 평균을 깁스 표본 기법을 이용하여 구하였고, 이로 부터 얻은 베이지안 추정량을 최소 자승 추정량, EM알고리즘을 이용한 랜덤 효과를 포함한 가능도함수에 대한 최대 가능도 추정량(MLR)과 비교하였다.

• Journal of the Korean Data and Information Science Society
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• 제16권4호
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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.

• Communications for Statistical Applications and Methods
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• 제9권1호
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• pp.155-166
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• 2002

Neural networks have been studied as a popular tool for classification and they are very flexible. Also, they are used for many applications of pattern classification and pattern recognition. This paper focuses on Bayesian approach to feed-forward neural networks with single hidden layer of units with logistic activation. In this model, we are interested in deciding the number of nodes of neural network model with p input units, one hidden layer with m hidden nodes and one output unit in Bayesian setup for fixed m. Here, we use the latent variable into the prior of the coefficient regression, and we introduce the 'sequential step' which is based on the idea of the data augmentation by Tanner and Wong(1787). The MCMC method(Gibbs sampler and Metropolish algorithm) can be used to overcome the complicated Bayesian computation. Finally, a proposed method is applied to a simulated data.

• 한국데이터정보과학회:학술대회논문집
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• 한국데이터정보과학회 2006년도 추계 학술발표회 논문집
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• pp.71-80
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• 2006

A nonparametric Bayesian multiple comparisons problem (MCP) for dependence parameters in I bivariate exponential populations is studied here. A simple method for pairwise comparisons of these parameters is also suggested. Here we extend the methodology studied by Gopalan and Berry (1998) using Dirichlet process priors. The family of Dirichlet process priors is applied in the form of baseline prior and likelihood combination to provide the comparisons. Computation of the posterior probabilities of all possible hypotheses are carried out through Markov Chain Monte Carlo method, namely, Gibbs sampling, due to the intractability of analytic evaluation. The whole process of MCP for the dependent parameters of bivariate exponential populations is illustrated through a numerical example.

• Journal of applied mathematics & informatics
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• 제9권1호
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• pp.289-301
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• 2002

This paper considers the Bayesian analysis of the regression model wish autoregressive errors. The Bayesian approach for finding the order p of autoregressive error is proposed and the proposed method can be simplified by generalized Savage-Dicky density ratio(Verdinelli and Wasser-man, [18]). And the Markov chain Monte Carlo method(Gibbs sample, [7]) is used in order to overcome the difficulty of Bayesian computations. Final1y, several examples are used to illustrate our proposed methodology.

• 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.