• The Korean Journal of Applied Statistics
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• v.26 no.3
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• pp.389-399
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• 2013

This article introduces Gaussian process regression and shows its application with time-course microarray gene expression data. Gene screening for yeast cell cycle microarray expression data is accomplished with a ratio of log marginal likelihood that uses Gaussian process regression with a squared exponential covariance kernel function. Gaussian process regression fitting with each gene is done and shown with the nine top ranking genes. With the screened data the Gaussian model-based clustering is done and its silhouette values are calculated for cluster validity.

• Structural Engineering and Mechanics
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• v.28 no.2
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• pp.129-152
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• 2008

This paper considers the solution of the stochastic differential equations (SDEs) with random operator and/or random excitation using the spectral SFEM. The random system parameters (involved in the operator) and the random excitations are modeled as second order stochastic processes defined only by their means and covariance functions. All random fields dealt with in this paper are continuous and do not have known explicit forms dependent on the spatial dimension. This fact makes the usage of the finite element (FE) analysis be difficult. Relying on the spectral properties of the covariance function, the Karhunen-Loeve expansion is used to represent these processes to overcome this difficulty. Then, a spectral approximation for the stochastic response (solution) of the SDE is obtained based on the implementation of the concept of generalized inverse defined by the Neumann expansion. This leads to an explicit expression for the solution process as a multivariate polynomial functional of a set of uncorrelated random variables that enables us to compute the statistical moments of the solution vector. To check the validity of this method, two applications are introduced which are, randomly loaded simply supported reinforced concrete beam and reinforced concrete cantilever beam with random bending rigidity. Finally, a more general application, randomly loaded simply supported reinforced concrete beam with random bending rigidity, is presented to illustrate the method.

• Journal of the Korean Institute of Telematics and Electronics
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• v.17 no.1
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• pp.1-9
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• 1980

In this paper several basic techniques for signal processing and analysis are surveyed. Firstly by the intervention of the uncertainty principle, an equality sign may have different degree of precision if non commutable operators are applied. Seconds y maximum entropy estimate and randam process based viewpoint must be enhanced to get rid of the well established and reigning deterministic image of science. Thirdly techniques for the analysis of a signal namely detection. ess]motion and modulation are explained as well as the positive definiteness of a covariance function, Karhunen-Loeve expansion and SVD of an image.

• Journal of Korean Institute of Industrial Engineers
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• v.29 no.2
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• pp.114-125
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• 2003

This paper proposes multivariate process capability indices (PCIs) for skewed populations using $T^2$rand modified process region approaches. The proposed methods are based on the multivariate version of a weighted standard deviation method which adjusts the variance-covariance matrix of quality characteristics and approximates the probability density function using several multivariate Journal distributions with the adjusted variance-covariance matrix. Performance of the proposed PCIs is investigated using Monte Carlo simulation, and finite sample properties of the estimators are studied by means of relative bias and mean square error.

• Wind and Structures
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• v.9 no.2
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• pp.159-178
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• 2006

For the slender and flexible cable supported bridges, identification of all the flutter derivatives for the vertical, lateral and torsional motions is essential for its stability investigation. In all, eighteen flutter derivatives may have to be considered, the identification of which using a three degree-of-freedom elastic suspension system has been a challenging task. In this paper, a system identification technique, known as covariance-driven stochastic subspace identification (COV-SSI) technique, has been utilized to extract the flutter derivatives for a typical bridge deck. This method identifies the stochastic state-space model from the covariances of the output-only (stochastic) data. All the eighteen flutter derivatives have been simultaneously extracted from the output response data obtained from wind tunnel test on a 3-DOF elastically suspended bridge deck section-model. Simplicity in model suspension and measurements of only output responses are additional motivating factors for adopting COV-SSI technique. The identified discrete values of flutter derivatives have been approximated by rational functions.

• Communications for Statistical Applications and Methods
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• v.9 no.1
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• pp.87-100
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• 2002

Poorly-posed problems in the balanced discriminant analysis was considered. We restrict consideration to the case of observations and the number of variables are the same and small. When these problems exist, we do not use a maximum likelihood estimates(MLE) to estimate covariance matrices. Instead of MLE, an alternative estimate for the covariance matrices are proposed. This alternative method make good use of two regularization parameters, $\lambda$} and $\gamma$. A new test rule for the discriminant function is suggested and examined via limited hut informative simulation study. From the simulation study, it is shown that the suggested test rule gives better test result than other previously suggested method in terms of error rate criterion.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.3 no.1
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• pp.29-34
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• 1999

In the paper, the extened Huygens-Fresnel principle has been used to make an analysis of the statistics the received intensity for speckle propagation though the turbulent atmosphere. The results of these formulations include of the log-amplitude covariance as well as the wave structure functions, and It was found that the normalized variance is dependent on the turblence strength and rises above unity.

• Communications for Statistical Applications and Methods
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• v.15 no.3
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• pp.333-342
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• 2008

Variable selection theorem in the linear regression model is extended to the analysis of covariance model. When some of regression variables are omitted from the model, it reduces the variance of the estimators but introduces bias. Thus an appropriate balance between a biased model and one with large variances is recommended.

• Communications of Mathematical Education
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• v.22 no.4
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• pp.417-444
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• 2008

Many research papers on the college students' functional concept show they have poor understanding on this topic. To compare the results with that of Korean students, four interrelated topics are chosen: How do they understand the concept of function?; what are their misconceptions including epistemological obstacles?; How do the function concepts develop and are acquired? For this a survey has been conducted to 95 engineering students just before they start Calculus course. We have done research on other major areas including psychology, economics and statistics to see how function is defined in these areas. Function definitions from US math text books are also introduced. Based on the these and the survey, some suggestions are made on the new curriculum which treat function as a correspondence relation. Vertical line test should be added to the Algebra II/Pre calculus course to check the univalent property.

• Korean Journal of Mathematics
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• v.25 no.1
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• pp.45-60
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• 2017

This paper focuses on estimation of an non-integral quadratic function (NIQF) and integral quadratic function (IQF) of a random signal in dynamic system described by a linear stochastic differential equation. The quadratic form of an unobservable signal indicates useful information of a signal for control. The optimal (in mean square sense) and suboptimal estimates of NIQF and IQF represent a function of the Kalman estimate and its error covariance. The proposed estimation algorithms have a closed-form estimation procedure. The obtained estimates are studied in detail, including derivation of the exact formulas and differential equations for mean square errors. The results we demonstrate on practical example of a power of signal, and comparison analysis between optimal and suboptimal estimators is presented.