• The Korean Journal of Applied Statistics
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• v.18 no.1
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• pp.67-81
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• 2005

Most of the previously proposed methods for the frailty model do not work well when there are many tied observations. This is partly because the empirical likelihood used is not suitable for tied observations. In this paper, we propose a new method for the frailty model with many ties. The proposed method obtains the posterior distribution of the parameters using the binomial form empirical likelihood and Bayesian bootstrap. The proposed method yields stable results and is computationally fast. To compare the proposed method with the maximum marginal likelihood approach, we do simulations.

• Journal of the Korean Society of Radiology
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• v.16 no.2
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• pp.151-156
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• 2022

A detector using a small number of photosensors was designed, and the position of a scintillation pixel that interacted with gamma rays through a maximum likelihood position estimation(MLPE) was measured as a digital position. For this purpose, simulation was performed using DETECT2000, which can simulate the movement of light within the scintillator, and the accuracy of position measurement was evaluated. A detector was configured using a 6 × 6 scintillation pixel array and 4 photosensors, and a gamma ray event was generated at the center of each scintillation pixel to create a look-up table through the ratio of acquired light. The gamma-ray event generated at the new position was applied as the input value of the MLPE, and the positiion of the scintillation pixel was converted into a digital positiion after comparison with the look-up table. All scintillation pixels were evaluated, and as a result, a high accuracy of 99.1% was obtained. When this method is applied to the currently usesd system, it is concidered that the process of determining the position of the scintillation pixel will be simplified.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.36 no.6
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• pp.391-398
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• 2023

In this paper, a penalized maximum likelihood estimation (PMLE) method that applies a penalty to increase the accuracy of a basis-screening-based Kriging model (BSKM) is introduced. The maximum order and set of basis functions used in the BSKM are determined according to their importance. In this regard, the cross-validation error (CVE) for the basis functions is employed as an indicator of importance. When constructing the Kriging model (KM), the maximum order of basis functions is determined, the importance of each basis function is evaluated according to the corresponding maximum order, and finally the optimal set of basis functions is determined. This optimal set is created by adding basis functions one by one in order of importance until the CVE of the KM is minimized. In this process, the KM must be generated repeatedly. Simultaneously, hyper-parameters representing correlations between datasets must be calculated through the maximum likelihood evaluation method. Given that the optimal set of basis functions depends on such hyper-parameters, it has a significant impact on the accuracy of the KM. The PMLE method is applied to accurately calculate hyper-parameters. It was confirmed that the accuracy of a BSKM can be improved by applying it to Branin-Hoo problem.

• Proceedings of the Korean Reliability Society Conference
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• 2000.11a
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• pp.315-320
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• 2000

본 연구에서는 수리 가능한 시스템에서 고장 강도와 수리 효과에 대한 모수 추정 문제를 다룬다. 시스템이 노후화로 인한 고장이 발생할 경우 최소수리가 행해지고 계획된 예방정비에서는 비례적 수명 감소가 이루어지는 수명 데이터에 대해서 고장 강도 함수의 모수와 정비의 수리효과를 추정하기 위해서 최대 우도 함수 방법을 이용한다. 또한 유전자 알고리즘을 이용해서 우도 함수를 최대화시키는 절차를 개발하고 수치 예제를 나타낸다.

• Journal of the Korean Data and Information Science Society
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• v.7 no.2
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• pp.263-272
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• 1996

In this parer, under random censorship model, an estimation of scale and shape parameters in Weibull lifetime model is considered. Based on nonparametric estimator of survival function, the least square method is proposed. The proposed estimation method is simple and the performance of the proposed estimator is as efficient as maximum likelihood estimators. An example is presented, using field winding data. Simulation studies are performed to compare the performaces of the proposed estimator and maximum likelihood estimator.

• The Journal of Engineering Geology
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• v.3 no.1
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• pp.51-61
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• 1993

Restricted maximum likelihood(RML) method was used to determine the parameters of generalized covariance, and universal krigig with RML was applied to estimate a groundwater level distribution of nonstationarv random function. Universal kriging with RML was compared to IRF-k with weighted least squares method for the comparison of their accuracies. Cross validation shows that two methods have nearly the same ability for the estimation of groundwater levels. Scattergram of estimates versus true values and contour maps of groundwater levels have nearly the same results. The reason why two methods produced the same results is thought to be the non-Gaussian distribution and the snaall number of sample data.

• Journal of the Korean Society of Radiology
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• v.15 no.4
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• pp.409-414
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• 2021

In order to acquire an image from a gamma camera, linearity correction must be performed. To this end, digital coordinates are acquired by using a linearity map to accurately specify the location where the scintillator and gamma rays interact. In this study, a method for acquiring undistorted images and digital coordinates was developed using a lookup table and maximum likelihood position estimation without using a linearity map. The proposed method was verified by configuring a small gamma camera through DETECT2000 simulation. A gamma camera was constructed using a GAGG scintillator and a SiPM optical sensor, and a gamma-ray interaction was generated at the center of the scintillator, and a lookup table was prepared using the ratio of the signals obtained from the SiPM. Through the prepared lookup table and the maximum likelihood position estimation, the position of the signal obtained by the gamma-ray interaction was acquired as digital coordinates to compose an image. As a result, the linearity was maintained compared to the generally acquired image, the accuracy of the location where the gamma-ray interaction was generated was excellent, and the distance between the locations was uniform. Since the lookup table obtained through simulation is created using the ratio of the signal, it can be directly used in the experiment, and the position of the signal can be conveniently obtained with digital coordinates with corrected linearity without creating a linearity map.

• The Korean Journal of Applied Statistics
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• v.28 no.5
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• pp.895-906
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• 2015

Diffusion is a mathematical tool to explain the fluctuation of financial assets and the movement of particles in a micro time scale. There are ongoing statistical trials to develop an estimation method for diffusion models based on likelihood. When we estimate diffusion models by applying the maximum likelihood estimation method on data observed at discrete time points, we need to know the transition density of the diffusion. In order to approximate the transition densities of diffusion models, we suggests the method to approximate the path integral of the random process with normal random variables, and compare the numerical properties of the method with other approximation methods.

• Journal of the Korean Society of Radiology
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• v.15 no.1
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• pp.1-7
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• 2021

In order to acquire an image in a positron emission tomography, it is necessary to draw the position coordinates of the scintillation pixels of the detector module measured at the same time. To this end, in a detector module using a plurality of scintillation pixels and a small number of photosensors, it is necessary to obtain a flood image and divide a region of each scintillation pixel to obtain a position of a scintillation pixel interacting with a gamma ray. Alternatively, when the number of scintillation pixels and the number of photosensors to be used are the same, the position coordinates for the position of the scintillation pixels can be directly acquired as digital signal coordinates. A method of using a plurality of scintillation pixels and a small number of photosensors requires a process of obtaining digital signal coordinates requires a plurality of photosensors and a signal processing system. This complicates the signal processing process and raises the cost. To solve this problem, in this study, we developed a method of obtaining digital signal coordinates without performing the process of separating the planar image and region using a plurality of flash pixels and a small number of optical sensors. This is a method of obtaining the position coordinate values of the flash pixels interacting with the gamma ray as a digital signal through a look-up table created through the signals acquired from each flash pixel using the maximum likelihood function. Simulation was performed using DETECT2000, and verification was performed on the proposed method. As a result, accurate digital signal coordinates could be obtained from all the flash pixels, and if this is applied to the existing system, it is considered that faster image acquisition is possible by simplifying the signal processing process.

• Journal of the Korean Data and Information Science Society
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• v.7 no.2
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• pp.257-262
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• 1996

When we are estimate the smoothing parameter in spline regression model, we deal the diagnostic of influence observations as posteriori analysis. When we use Generalized Maximum Likelihood Function as the estimation method of smoothing parameter, we propose the diagnostic measure for influencial observations in the obtained estimate, and we introduce the finding method of the proper smoothing parameter estimate.