• Journal of the Chungcheong Mathematical Society
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• v.12 no.1
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• pp.133-146
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• 1999

Let {X(t), $t{\geq}0$} be a stochastic integral process represented by stable random measure or multiple Ito-Wiener integrals. Under some conditions, we prove the continuity and self-similarity of these stochastic integral processes. As an application, we get Gaussian chaos which has some shift continuous function.

• Journal of the Korean Mathematical Society
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• v.53 no.5
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• pp.991-1017
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• 2016

In this paper we define a generalized analytic Fourier-Feynman transform associated with Gaussian process on the function space $C_{a,b}[0,T]$. We establish the existence of the generalized analytic Fourier-Feynman transform for certain bounded functionals on $C_{a,b}[0,T]$. We then proceed to establish a translation theorem for the generalized transform associated with Gaussian process.

• Journal of the Korean Mathematical Society
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• v.42 no.6
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• pp.1265-1278
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• 2005

In this paper, we establish limit theorems containing both the moduli of continuity and the large incremental results for finite dimensional Gaussian processes with N parameters, via estimating upper bounds of large deviation probabilities on suprema of the Gaussian processes.

• Proceedings of the Korean Information Science Society Conference
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• 2007.10c
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• pp.485-489
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• 2007

Gaussian process classifiers (GPCs) are fully statistical kernel classification models which have a latent function with Gaussian process prior Recently, EP approximation method has been proposed to infer the posterior over the latent function. It can have a special hyperparameter which can treat outliers potentially. In this paper, we propose the outlier robust algorithm which alternates EP and the hyperparameter updating until convergence. We also show its usefulness with the simulation results.

• Nuclear Engineering and Technology
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• v.52 no.8
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• pp.1807-1816
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• 2020

In this work, a Gaussian Process (Kriging) approach is proposed to provide efficient dose mapping for complex radiation fields using limited number of responses. Given a few response measurements (or simulation data points), the proposed approach can help the analyst in completing a map of the radiation dose field with a 95% confidence interval, efficiently. Two case studies are used to validate the proposed approach. The First case study is based on experimental dose measurements to build the dose map in a radiation field induced by a D-D neutron generator. The second, is a simulation case study where the proposed approach is used to mimic Monte Carlo dose predictions in the radiation field using a limited number of MCNP simulations. Given the low computational cost of constructing Gaussian Process (GP) models, results indicate that the GP model can reasonably map the dose in the radiation field given a limited number of data measurements. Both case studies are performed on the nuclear engineering radiation laboratories at the University of Sharjah.

• Journal of the Semiconductor & Display Technology
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• v.11 no.3
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• pp.19-25
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• 2012

The accuracy of Shape From Focus (SFF) technique depends on the quality of the focus measurements which are computed through a focus measure operator. In this paper, we introduce a new approach to estimate 3D shape of an object based on Gaussian process regression. First, initial depth is estimated by applying a conventional focus measure on image sequence and maximizing it in the optical direction. In second step, input feature vectors consisting of eginvalues are computed from 3D neighborhood around the initial depth. Finally, by utilizing these features, a latent function is developed through Gaussian process regression to estimate accurate depth. The proposed approach takes advantages of the multivariate statistical features and covariance function. The proposed method is tested by using image sequences of various objects. Experimental results demonstrate the efficacy of the proposed scheme.

• Proceedings of the Korean Statistical Society Conference
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• 2000.11a
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• pp.115-118
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• 2000

In this paper we establish limit results on the increments of (N, d)-Gaussian processes with independent components, via estimating upper bounds of large deviation probabilities on the suprema of (N, d)-Gaussian processes.

• Journal of the Korean Mathematical Society
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• v.36 no.4
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• pp.679-679
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• 1999

• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.269-279
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• 2003

We prove an empirical LIL for the Kaplan-Meier integral process constructed from the random censorship model under bracketing entropy and mild assumptions due to censoring effects. The main method in deriving the empirical LIL is to use a weak convergence result of the sequential Kaplan-Meier integral process whose proofs appear in Bae and Kim [2]. Using the result of weak convergence, we translate the problem of the Kaplan Meier integral process into that of a Gaussian process. Finally we derive the result using an empirical LIL for the Gaussian process of Pisier [6] via a method adapted from Ossiander [5]. The result of this paper extends the empirical LIL for IID random variables to that of a random censorship model.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.39 no.1
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• pp.64-72
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• 2016

In this paper, we utilize a Gaussian process to predict the power consumption in the air-conditioning system. As the power consumption in the air-conditioning system takes a form of a time-series and the prediction of the power consumption becomes very important from the perspective of the efficient energy management, it is worth to investigate the time-series model for the prediction of the power consumption. To this end, we apply the Gaussian process to predict the power consumption, in which the Gaussian process provides a prior probability to every possible function and higher probabilities are given to functions that are more likely consistent with the empirical data. We also discuss how to estimate the hyper-parameters, which are parameters in the covariance function of the Gaussian process model. We estimated the hyper-parameters with two different methods (marginal likelihood and leave-one-out cross validation) and obtained a model that pertinently describes the data and the results are more or less independent of the estimation method of hyper-parameters. We validated the prediction results by the error analysis of the mean relative error and the mean absolute error. The mean relative error analysis showed that about 3.4% of the predicted value came from the error, and the mean absolute error analysis confirmed that the error in within the standard deviation of the predicted value. We also adopt the non-parametric Wilcoxon's sign-rank test to assess the fitness of the proposed model and found that the null hypothesis of uniformity was accepted under the significance level of 5%. These results can be applied to a more elaborate control of the power consumption in the air-conditioning system.