• Communications for Statistical Applications and Methods
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• v.9 no.1
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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.

• Communications for Statistical Applications and Methods
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• v.8 no.1
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• pp.159-171
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• 2001

Shapiro and Wilk (1972) developed a test for exponentiality with origin and scale unknown. The procedure consists of comparing the generalized least squares estimate of scale with the estimate of scale given by the sample variance. However the test statistic is inconsistent ; that is, the power of the test will not approach 1 as the sample size increases. Hence we give a test based on the ratio of two asymptotically efficient estimates of scale. We also have conducted a power study to compare the test procedures, using Monte Carlo samples from a wide range of alternatives. It is found that the suggested statistics have higher power for the alternatives with the coefficient of variation greater that or equal to 1.

• Proceedings of the Korean Statistical Society Conference
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• 2005.11a
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• pp.59-65
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• 2005

We propose five Bayesian methods to estimate the cell expectation in an incomplete multi-way categorical table with nonignorable nonresponse mechanism. We study 3 Bayesian methods which were previously applied to one-way categorical tables. We extend them to multi-way tables and, in addition, develop 2 new Bayesian methods for multi-way categorical tables. These five methods are distinguished by different priors on the cell probabilities: two of them have the priors determined only by information of respondents; one has a constant prior; and the remaining two have priors reflecting the difference in the response mechanisms between respondent and non-respondent. We also compare the five Bayesian methods using a categorical data for a prospective study of pregnant women.

• Journal of the Korean Statistical Society
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• v.28 no.2
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• pp.167-182
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• 1999

This article is concerned with the selection of subsets of predictor variables to be included in building the binary response probit regression model. It is based on a Bayesian approach, intended to propose and develop a procedure that uses probabilistic considerations for selecting promising subsets. This procedure reformulates the probit regression setup in a hierarchical normal mixture model by introducing a set of hyperparameters that will be used to identify subset choices. The appropriate posterior probability of each subset of predictor variables is obtained through the Gibbs sampler, which samples indirectly from the multinomial posterior distribution on the set of possible subset choices. Thus, in this procedure, the most promising subset of predictors can be identified as the one with highest posterior probability. To highlight the merit of this procedure a couple of illustrative numerical examples are given.

• Communications for Statistical Applications and Methods
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• v.7 no.1
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• pp.65-86
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• 2000

The estimates from an EM when it is applied to a large causal model of 10 or more categorical variables are often subject to the initial values for the estimates. This phenomenon becomes more serious as the model structure becomes more serious as the model structure becomes more complicated involving more variables. In this regard Wu(1983) recommends among others that EMs are implemented several times with different sets of initial values to obtain more appropriate estimates. in this paper a new approach for initial values is proposed. The main idea is that we use initials that are calibrated to data. A simulation result strongly indicates that the calibrated initials give rise to the estimates that are far closer to the true values than the initials that are not calibrated.

• Communications for Statistical Applications and Methods
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• v.7 no.3
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• pp.845-858
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• 2000

In this paper new results are obtained for multivariate processes which help us to identify weak negative orthant dependent(WNOD) structures among hitting times of the processes. Furthermore, an approach to derive dependence properties among the processes is proposed and a partial solution to the question tat what kinds of the dependence properties, when they are imposed on processes, are reflected as analogous properties of corresponding hitting times is give. Examples are given to illustrate these concepts.

• Journal of the Korean Statistical Society
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• v.7 no.1
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• pp.27-43
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• 1978

This paper deals with the problem of obtaining a minimum cost acceptance sampling plan for destructive testing. The cost model is constructed under the assumption that the sampling procedure takes the following form; 1) lots rejected on the first sample are acreened with a non-destructive testing, 2) the screening is assumed to be imperfect, and therefore, after the screening, a second sample is taken to determine whether to accept the lot of to scrap it. The usual sampling procedures for destructive testing can be regarded as special cases of the above one. Utilizing Hald's Bayesian approach, procedures for finding the global optimal sampling plans are given. However, when the lot size is large, the global plan is very different to obtain even with the aid of an electronic computer. Therefore a method of finding suboptimal plan is suggested. An example with uniform prior is also given.

• Journal of the Korean Statistical Society
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• v.36 no.1
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• pp.157-173
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• 2007

In this article it is considered that how the slope-rotatability property of a second order design for response surface model is affected by block effects and how the design points are assigned into the blocks so that the blocked design may have the property of slope-rotatability. If an unblocked design is blocked properly, it could be a slope-rotatable design with block effects and this property is named as block slope-rotatability. We approach this problem from the moment matrix of the blocked design, which plays an important role to get the variances of the estimates, and suggest conditions of block slope-rotatability.

• Communications for Statistical Applications and Methods
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• v.23 no.2
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• pp.105-117
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• 2016

In the paper, as a sequence of the first tutorial, we discuss sufficient dimension reduction methodologies used to estimate central subspace (sliced inverse regression, sliced average variance estimation), central mean subspace (ordinary least square, principal Hessian direction, iterative Hessian transformation), and central $k^{th}$-moment subspace (covariance method). Large-sample tests to determine the structural dimensions of the three target subspaces are well derived in most of the methodologies; however, a permutation test (which does not require large-sample distributions) is introduced. The test can be applied to the methodologies discussed in the paper. Theoretical relationships among the sufficient dimension reduction methodologies are also investigated and real data analysis is presented for illustration purposes. A seeded dimension reduction approach is then introduced for the methodologies to apply to large p small n regressions.

• Communications for Statistical Applications and Methods
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• v.23 no.2
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• pp.93-103
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• 2016

In the paper, we discuss dimension reduction of predictors ${\mathbf{X}}{\in}{{\mathbb{R}}^p}$ in a regression of $Y{\mid}{\mathbf{X}}$ with a notion of sufficiency that is called sufficient dimension reduction. In sufficient dimension reduction, the original predictors ${\mathbf{X}}$ are replaced by its lower-dimensional linear projection without loss of information on selected aspects of the conditional distribution. Depending on the aspects, the central subspace, the central mean subspace and the central $k^{th}$-moment subspace are defined and investigated as primary interests. Then the relationships among the three subspaces and the changes in the three subspaces for non-singular transformation of ${\mathbf{X}}$ are studied. We discuss the two conditions to guarantee the existence of the three subspaces that constrain the marginal distribution of ${\mathbf{X}}$ and the conditional distribution of $Y{\mid}{\mathbf{X}}$. A general approach to estimate them is also introduced along with an explanation for conditions commonly assumed in most sufficient dimension reduction methodologies.