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Reference Priors in a Two-Way Mixed-Effects Analysis of Variance Model
장인홍,김병휘,Chang, In-Hong,Kim, Byung-Hwee The Korean Data and Information Science Society 2002 한국데이터정보과학회지 Vol.13 No.2
We first derive group ordering reference priors in a two-way mixed-effects analysis of variance (ANOVA) model. We show that posterior distributions are proper and provide marginal posterior distributions under reference priors. We also examine whether the reference priors satisfy the probability matching criterion. Finally, the reference prior satisfying the probability matching criterion is shown to be good in the sense of frequentist coverage probability of the posterior quantile.
확률사상들의 독립성과 배반성 및 확률변수들의 독립성과 무상관성에 대하여
장인홍,박태룡 한국수학사학회 2002 Journal for history of mathematics Vol.15 No.2
In this paper, we explain independence and mutually exclusiveness of events. Also we explain independence and uncorrelation of random variables. Finally we compare with differences as examples.
장인홍 한국수학사학회 2002 Journal for history of mathematics Vol.15 No.3
In this paper we investigate an origin and development of the classical theory of probability. And we also investigate the law of large numbers and central limit theorem which are very important in tile probability theory.
무정보 사전분포를 이용한 이원배치 혼합효과 분산분석모형에서 오차분산에 대한 베이지안 분석
장인홍,김병휘 한국통계학회 2002 응용통계연구 Vol.15 No.2
반복이 같은 이원배치 혼합효과 분산분석모형에서 무정보 사전분포를 이용하여 오차분산을 추정하는 문제를 생각하고자 한다. 먼저 무정보 사전분포로 제프리스사전분포, 준거 사전분포 그리고 확률일치 사전분포를 유도하고 이들 각각의 사전분포들에 대하여 주변사후분포를 제시하였다. 끝으로 실제 자료를 근거로 오차분산의 주변사후밀도함수에 대한 그래프와 오차분산에 대한 신용구간들을 구하고 이 구간들을 비교한다. We consider the problem of estimating the error variance of in a two-way mixed-effects ANOVA model using noninformative priors. First, we derive Jeffreys' prior, a reference prior, and matching priors. We then provide marginal posterior distributions under those noninformative priors. Finally, we provide graphs of marginal posterior densities of the error variance and credible intervals for the error variance in two real data set and compare these credible intervals.
NHPP소프트웨어 신뢰도 성장모형에서 베이지안 모수추정과 예측
장인홍,장덕환,이승우,송광윤 한국데이터정보과학회 2013 한국데이터정보과학회지 Vol.24 No.4
In this paper we consider the NHPP software reliability model. And we deal with the maximum likelihood estimation and the Bayesian estimation with conjugate prior for parameter inference in the mean value function of Goel-Okumoto model (1979). The parameter estimates for the proposed model is presented by MLE and Bayes estimator in data set. We compare the predicted number of faults with the actual data set using the proposed mean value function. 본 논문은 NHPP 소프트웨어 신뢰성모형에서 모수추정과 고장시간에 대한 예측을 다루고자 한다. 소프트웨어 신뢰성모형 Goel-Okumoto모형에서 평균값 함수에 대한 최우추정과 경험적 사전분포를 가정한 공액사전분포에서 베이지안 추정을 다루었다. 실제 자료에서 두 가지 추정법에 의한 모수 추정값을 제공하였으며, 모형의 적합성을 판정하고, 고장수에 대한 예측값을 비교하였다.
Bayesian reliability estimation in a stress-strength system
장인홍,오수진 한국신뢰성학회 2011 신뢰성응용연구 Vol.11 No.2
We consider the problem of estimating the system reliability using noninformative priors when both stress and strength follow generalized gamma distributions with index, scale, and shape parameters. We first derive group-ordering reference priors using the reparametrization. We next provide the sufficient condition for propriety of posterior distributions and provide marginal posterior distributions under those noninformative priors. Finally, we provide and compare estimated values of the system reliability based on the simulated values of parameter of interest in some special cases.
2원배치 혼합 선형 모형에서 오차 분산의 개선된 추정량들
김병휘,장인홍 漢陽大學校 自然科學硏究所 1999 自然科學論文集 Vol.18 No.-
반복수가 같은 2원 배치 혼합 선형 모형에서 가중치 자승 오차 손실 함수를 사용하여 기존에 사용되고 있는 오차 분산의 최소최대 추정량을 위험 함수의 관점에서 개선하는 오차분산의 새로운 최소최대 추정량들을 Stein(1964)의 개념을 이용하여 제공하고자 한다. For estimating the error variance in a balanced two-way mixed linear model, we provide, using Stein's(1964) ideas, a class of new minimax estimators, which dominate the usual minimax estimator in view of the risk function, under the weighted squared error loss.
Chang, In-Hong 조선대학교 통계연구소 1999 統計硏究所論文誌 Vol.1 No.1
Consider the problem of estimating a vector of unknown regression coefficients or an unknown estimable function under the sum of squared error losses in linear models. We first provide empirical and hierarchical Bayes estimators of an estimable function shrinking towards a fixed known point. We also show that the empirical Bayes estimator of an estimable function is identical to the James-Stein estimator of the same estimable function and the hierarchical Bayes estimator of an estimable function is identical to the least squares estimator of the same estimable function.
김윤수,장인홍,송광윤 조선대학교 기초과학연구원 2024 조선자연과학논문집 Vol.17 No.1
Many abnormal climate events are occurring around the world. The cause of abnormal climate is related to temperature. Factors that affect temperature include excessive emissions of carbon and greenhouse gases from a global perspective, and air circulation from a local perspective. Due to the air circulation, many abnormal climate phenomena such as abnormally high temperature and abnormally low temperature are occurring in certain areas, which can cause very serious human damage. Therefore, the problem of abnormal temperature should not be approached only as a case of climate change, but should be studied as a new category of climate crisis. In this study, we proposed a model for the classification of abnormal temperature using random forests based on various meteorological data such as longitudinal observations, yellow dust, ultraviolet radiation from 2018 to 2022 for each region in Korea. Here, the meteorological data had an imbalance problem, so the imbalance problem was solved by oversampling. As a result, we found that the variables affecting abnormal temperature are different in different regions. In particular, the central and southern regions are influenced by high pressure (Mainland China, Siberian high pressure, and North Pacific high pressure) due to their regional characteristics, so pressure-related variables had a significant impact on the classification of abnormal temperature. This suggests that a regional approach can be taken to predict abnormal temperatures from the surrounding meteorological environment. In addition, in the event of an abnormal temperature, it seems that it is possible to take preventive measures in advance according to regional characteristics.