• The Korean Journal of Applied Statistics
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• v.14 no.2
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• pp.449-462
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• 2001

베이지안 다중 검정방법(multiple hypothesis test)은 여러 통계모형에서 성공적인 결과를 주는 것으로 알려져있다. 일반적으로, 베이지안 가설검정은 고려중인 모형에 대한 사후확률을 계산하여 가장 높은 확률은 갖는 모형을 선택하기 때문에 귀무가설의 기각여부에만 관심을 가지는 고전적인 분산분석 검정과는 달리 좀 더 구체적인 모형을 선택할 수 있는 장점이 있다. 이 논문에서는 독립이면서 로그정규분포를 따르는 K($\geq$3)개 모집단의 모수에 대한 가설 검정방법으로 O’Hagan(1995)이 제안한 부분 베이즈 요인을 이용한 베이지안 방법을 제안한다. 이 때 모수에 대한 사전분포로는 무정보적 사전분포를 사용한다. 제안한 검정 방법의 유용성을 알아보기 위하여 실제 자료의 분석과 모의 실험을 이용하여 고전적인 검정방법과 그 결과를 비교한다.

• Journal of Korean Society for Quality Management
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• v.28 no.1
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• pp.119-131
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• 2000

This paper suggests a new diagnostic measure for detecting influential observations in linear discriminant analysis (LDA). It is developed from a Bayesian point of view using a default Bayes factor obtained from the imaginary training sample methodology. The Bayes factor is taken as a criterion for testing homogeneity of covariance matrices in LDA model. It is noted that the effect of an observation over the criterion is fully explained by the diagnostic measure. We suggest a graphical method that can be taken as a tool for interpreting the diagnostic measure and detecting influential observations. Performance of the measure is examined through an illustrative example.

• Communications for Statistical Applications and Methods
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• v.6 no.1
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• pp.237-249
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• 1999

It has been issued that the irreconcilability of the classical test for a point null and standard Bayesian formulation for testing such a point null. The infimum of the posterior probability of the null hypothesis is used as measure of evidence against the null hypothesis in Bayesian approach; here the infimum is over the family of priors on the alternative hypotheses which includes all density that are a priori reasonable. For iid observations from a multivariate normal distribution in $\textit{p}$ dimensions with an unknown mean and a covariance matrix propotional to the Identity we consider the difference and the Wolfowitz distance of the distributions of the P-value and the lower bound of the posterior probability over the family of all normal priors. The Wolfowitz distance is interpreted as the average difference of the quantiles of the two distrbutions.

• Journal of the Korean Data and Information Science Society
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• v.28 no.1
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• pp.207-215
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• 2017

In this paper we study pooling effects in Bayesian testing procedures of independence for contingency tables from small areas. In small area estimation setup, we typically use a hierarchical Bayesian model for borrowing strength across small areas. This techniques of borrowing strength in small area estimation is used to construct a Bayes test of independence for contingency tables from small areas. In specific, we consider the methods of direct or indirect pooling in multinomial models through Dirichlet priors. We use the Bayes factor (or equivalently the ratio of the marginal likelihoods) to construct the Bayes test, and the marginal density is obtained by integrating the joint density function over all parameters. The Bayes test is computed by performing a Monte Carlo integration based on the method proposed by Nandram and Kim (2002).

• Journal of the Korean Statistical Society
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• v.32 no.4
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• pp.425-448
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• 2003

Meta-analysis refers to quantitative methods for combining results from independent studies in order to draw overall conclusions. We consider hierarchical models including selection models under a skewed heavy tailed error distribution proposed originally by Chen et al. (1999) and Branco and Dey (2001). These rich classes of models combine the information of independent studies, allowing investigation of variability both between and within studies, and incorporate weight function. Here, the testing for the skewness parameter is discussed. The score test statistic for such a test can be shown to be expressed as the posterior expectations. Also, we consider the detail computational scheme under skewed normal and skewed Student-t distribution using MCMC method. Finally, we introduce one example from Johnson (1993)'s real data and apply our proposed methodology. We investigate sensitivity of our results under different skewed errors and under different prior distributions.

• Journal of the Korean Statistical Society
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• v.28 no.1
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• pp.73-92
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• 1999

In Bayesian model selection or testing problems, one cannot utilize standard or default noninformative priors, since these priors are typically improper and are defined only up to arbitrary constants. The resulting Bayes factors are not well defined. A recently proposed model selection criterion, the intrinsic Bayes factor overcomes such problems by using a part of the sample as a training sample to get a proper posterior and then use the posterior as the prior for the remaining observations to compute the Bayes factor. Surprisingly, such Bayes factor can also be computed directly from the full sample by some proper priors, namely intrinsic priors. The present paper explains how to derive intrinsic priors for simple tree ordered exponential means. Some numerical results are also provided to support theoretical results and compare with classical methods.

• Journal of the Korean Mathematical Society
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• v.59 no.2
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• pp.217-233
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• 2022

Although machine learning shows state-of-the-art performance in a variety of fields, it is short a theoretical understanding of how machine learning works. Recently, theoretical approaches are actively being studied, and there are results for one of them, margin and its distribution. In this paper, especially we focused on the role of margin in the perturbations of inputs and parameters. We show a generalization bound for two cases, a linear model for binary classification and neural networks for multi-classification, when the inputs have normal distributed random noises. The additional generalization term caused by random noises is related to margin and exponentially inversely proportional to the noise level for binary classification. And in neural networks, the additional generalization term depends on (input dimension) × (norms of input and weights). For these results, we used the PAC-Bayesian framework. This paper is considering random noises and margin together, and it will be helpful to a better understanding of model sensitivity and the construction of robust generalization.

• Journal of Veterinary Clinics
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• v.24 no.2
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• pp.77-81
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• 2007

Diagnostic performance of polymerase chain reaction (PCR) for detecting Dirofilaria immitis in dogs was evaluated when no gold standard test was employed. An enzyme-linked immunosorbent assay test kit (SnapTM, IDEXX, USA) with unknown parameters was also employed. The sensitivity and specificity of the PCR from two-population model were estimated by using both maximum likelihood using expectation-maximization (EM) algorithm and Bayesian method, assuming conditional independence between the two tests. A total of 266 samples, 133 samples in each trial, were randomly retrieved from the heartworm database records during the year 2002-2004 in a university animal hospital. These data originated from the test results of military dogs which were brought for routine medical check-up or testing for heartworm infection. When combined 2 trials, sensitivity and specificity of the PCR was 96.4-96.7% and 97.6-98.8% in EM and 94.4-94.8% and 97.1-98% in Bayesian. There were no statistical differences between estimates. This finding indicates that the PCR assay could be useful screening tool for detecting heartworm antigen in dogs. This study was provided further evidences that Bayesian approach is an alternative approach to draw better inference about the performance of a new diagnostic test in case when either gold test is not available.

• Journal of Korean Society for Quality Management
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• v.16 no.2
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• pp.68-81
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• 1988

Testing procedures for a detection of change point in the regression model with correlated errors are discussed. A Bayesian approach is adopted and applied to a regression model with errors following an AR(1) model.

• Journal of the Korean Statistical Society
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• v.25 no.4
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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 .