• Journal of the Korean Data and Information Science Society
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• v.19 no.2
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• pp.577-585
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• 2008

This paper suggests a marginal probability model for analyzing repeated polytomous response data when some factors are nested in others in treatment structures on a larger experimental unit. As a repeated measures factor, time is considered on a smaller experimental unit. So, two different experiment sizes are considered. Each size of experimental unit has its own design structure and treatment structure, and the marginal probability model can be constructed from the structures for each size of experimental unit. Weighted least squares(WLS) methods are used for estimating fixed effects in the suggested model.

• The Korean Journal of Applied Statistics
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• v.14 no.1
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• pp.25-37
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• 2001

The marginal model is proposed for the analysis of data which have c(2: 3) categories in the 3 x 3 cross-over trials with three periods and three treatments. This model could be used for the counterpart of the Kenward-Jones' joint probability one and should be the generalization of Balagtas et ai's univariate marginal logits one, which analyze the treatment effects in the 3 x 3 cross-over trials with binary response variables[Kenward and Jones(1991), Balagtas et al(1995)]. The model equations for the marginal probability are constructed by the three types of link functions. The methods would be given for making of the link function matrices and model ones, and the estimation of parameters shall be discussed. The proposed model is applied to the analysis of Kenward and Jones' data.

• Communications for Statistical Applications and Methods
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• v.27 no.6
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• pp.675-688
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• 2020

In survival analysis of observational data, the inverse probability weighting method and the Cox proportional hazards model are widely used when estimating the causal effects of multiple-valued treatment. In this paper, the two kinds of weights have been examined in the inverse probability weighting method. We explain the reason why the stabilized weight is more appropriate when an inverse probability weighting method using the generalized propensity score is applied. We also emphasize that a marginal hazard ratio and the conditional hazard ratio should be distinguished when defining the hazard ratio as a treatment effect under the Cox proportional hazards model. A simulation study based on real data is conducted to provide concrete numerical evidence.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.265-270
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• 2007

The modern approach for wavelets imposes a Bayesian prior model on the wavelet coefficients to capture the sparseness of the wavelet expansion. The idea is to build flexible probability models for the marginal posterior densities of the wavelet coefficients. In this note, we derive exact expressions for a popular model for the marginal posterior density.

• Journal of the Korean Data and Information Science Society
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• v.13 no.2
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• pp.317-328
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• 2002

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.

• Journal of Korean Society of Rural Planning
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• v.24 no.2
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• pp.109-114
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• 2018

In this study, we estimate the greenhouse farmers' willingness to pay of agricultural water supply through pipeline. First, in the questionnaire design, orthogonal design and block design were used to enhance the ease of survey. Second, the theoretical model was constructed through the setting of the probability utility function, and the parameters were estimated by using the conditional logit model. Third, all of the estimation coefficients were statistically significant at the 1% significance level. The results of analysis are summarized as follows. First, the probability of selection is increased when maintenance is carried out by Korea Rural Community Corporation or local government. Second, the probability of selection is increased when agricultural water supply through pipeline is higher than the current level. Third, if the Korea Rural Community Corporation carries out maintenance management, the marginal willingness to pay is 44 won per ton. And if the local government carries out maintenance management, the marginal willingness to pay is 25 won per ton. Fourth, according to the quality level of agricultural water supply, the marginal willingness to pay is 101 won, 114 won and 120 won per ton, respectively. This study can be used as a basic data on the cost setting for agricultural water supply through pipeline.

• Journal of the Korean Statistical Society
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• v.29 no.1
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• pp.95-108
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• 2000

Consider the oblique factor model X=Af＋$\varepsilon$, with defining relation $\Sigma$=Λ$\Phi$Λ'＋Ψ. This paper is concerned with suggesting an optimal Bayes criterion for determining the number of factors in the model, i.e. dimension of the vector f. The use of marginal likelihood as a method for calculating posterior probability of each model with given dimension is developed under a generalized conjugate prior. Then based on an appropriate loss function, a Bayes rule is developed by use of the posterior probabilities. It is shown that the approach is straightforward to specify distributionally and to imploement computationally, with output readily adopted for constructing required cirterion.

• The Korean Journal of Applied Statistics
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• v.15 no.2
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• pp.405-414
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• 2002

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.

• Nuclear Engineering and Technology
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• v.53 no.2
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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.

• Ocean Systems Engineering
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• v.9 no.3
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• pp.287-328
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• 2019

Comprehensive understanding of the flood risk assessments via frequency analysis often demands multivariate designs under the different notations of return periods. Flood is a tri-variate random consequence, which often pointing the unreliability of univariate return period and demands for the joint dependency construction by accounting its multiple intercorrelated flood vectors i.e., flood peak, volume & durations. Selecting the most parsimonious probability functions for demonstrating univariate flood marginals distributions is often a mandatory pre-processing desire before the establishment of joint dependency. Especially under copulas methodology, which often allows the practitioner to model univariate marginals separately from their joint constructions. Parametric density approximations often hypothesized that the random samples must follow some specific or predefine probability density functions, which usually defines different estimates especially in the tail of distributions. Concentrations of the upper tail often seem interesting during flood modelling also, no evidence exhibited in favours of any fixed distributions, which often characterized through the trial and error procedure based on goodness-of-fit measures. On another side, model performance evaluations and selections of best-fitted distributions often demand precise investigations via comparing the relative sample reproducing capabilities otherwise, inconsistencies might reveal uncertainty. Also, the strength & weakness of different fitness statistics usually vary and having different extent during demonstrating gaps and dispensary among fitted distributions. In this literature, selections efforts of marginal distributions of flood variables are incorporated by employing an interactive set of parametric functions for event-based (or Block annual maxima) samples over the 50-years continuously-distributed streamflow characteristics for the Kelantan River basin at Gulliemard Bridge, Malaysia. Model fitness criteria are examined based on the degree of agreements between cumulative empirical and theoretical probabilities. Both the analytical as well as graphically visual inspections are undertaken to strengthen much decisive evidence in favour of best-fitted probability density.