• Communications for Statistical Applications and Methods
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• v.3 no.2
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• pp.291-298
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• 1996

통계학분야 그리고 또 다른 많은 분야에서 수치적 계산을 다루는 문제가 자주 발생한다. 적당한 컴퓨터 컴퓨터 시간안에 상당한 정도의 정확성을 줄 수 있고 또한 보다 광범위하게 사용 가능한 유용한 알고리즘의 필요성을 느낀다. 이러한 문제에 가능한 하나의 몬테칼로 알고리즘인 주표본 알고리즘을 소개하였다. 그리고 특히 본 눈문에서는 축차확률비검정의 오차확률을 계산하는 곳에 주표본 알고리즘을 적용하고 결과를 비교분석하였다.

• Communications for Statistical Applications and Methods
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• v.3 no.1
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• pp.169-177
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• 1996

본 논문에서는 한 유명 농구선수의 과거의 연도별 평균득점과 평균 야투율을 기초로 앞으로의 경기에 대한 평균득점과 평균야투율을 추정하기 위해 몬테칼로 베이지안 분석법 중의 하나인 Sampling-Important-Resampling (SIR) 알고리즘을 이용하였다. 즉 과거의 자료로부터 평균득점과 평균야투율에 대한 사전밀도함수를 설정하고 SIR 알고리즘을 이용하여 사후 밀도함수를 구한 후에 이를 기초로 베이지안 추론을 하였다.

• Proceedings of the Korean Statistical Society Conference
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• 2000.11a
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• pp.135-140
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• 2000

베이지안 신경망 모형(Bayesian Neural Networks Models)에서 주어진 입력값(input)은 블랙 박스(Black-Box)와 같은 신경망 구조의 각 층(layer)을 거쳐서 출력값(output)으로 계산된다. 새로운 입력 데이터에 대한 예측값은 사후분포(posterior distribution)의 기대값(mean)에 의해 계산된다. 주어진 사전분포(prior distribution)와 학습데이터에 의한 가능도함수(likelihood functions)를 통해 계산되어진 사후분포는 매우 복잡한 구조를 갖게 됨으로서 기대값의 적분계산에 대한 어려움이 발생한다. 이때 확률적 추정에 의한 근사 방법인 몬테칼로 적분을 이용한다. 이러한 방법으로서 Hybrid Monte Carlo 알고리즘은 우수한 결과를 제공하여준다(Neal 1996). 본 논문에서는 Hybrid Monte Carlo 알고리즘과 기존에 많이 사용되고 있는 Gibbs sampling, Metropolis algorithm, 그리고 Slice Sampling등의 몬테칼로 방법들을 비교한다.

• The Korean Journal of Applied Statistics
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• v.13 no.1
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• pp.45-53
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• 2000

본 논문에서는 모든 판정자(judge)들이 모든 객체(object)들에 대해 순위를 부여할 수 없는 경우에 얻어지는 불완전 순위자료에서 판정자들의 처리 효과에 대한 유의성을 검정하는데 관심이 있다. 이를 위해 불완전 순위자료를 완전자료로 바꾸는 알고리즘을 제안하고 알고리즘에 의해 얻어진 완전 순위자료에 Friedman 검정법을 적용하고자 한다. 제안된 검정법은 결측 객체에 순위를 부여하는데 있어서 완전순위를 갖는 판정자들의 정보를 이용함으로서 효율적이며 검정을 시행하는데 기존의 Friedman 통계량에 대한 분포표를 사용할 수 있어 간편하다. 그리고 몬테칼로 모의실험을 통하여 제안된 검정법과 기존의 평균 순위법, 최대/최소 Friedman 검정법과 검정력을 비교하였다.

• Radiation Oncology Journal
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• v.28 no.4
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• pp.238-248
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• 2010

Purpose: To compare the dose distributions between three-dimensional (3D) and four-dimensional (4D) radiation treatment plans calculated by Ray-tracing or the Monte Carlo algorithm, and to highlight the difference of dose calculation between two algorithms for lung heterogeneity correction in lung cancers. Materials and Methods: Prospectively gated 4D CTs in seven patients were obtained with a Brilliance CT64-Channel scanner along with a respiratory bellows gating device. After 4D treatment planning with the Ray Tracing algorithm in Multiplan 3.5.1, a CyberKnife stereotactic radiotherapy planning system, 3D Ray Tracing, 3D and 4D Monte Carlo dose calculations were performed under the same beam conditions (same number, directions, monitor units of beams). The 3D plan was performed in a primary CT image setting corresponding to middle phase expiration (50%). Relative dose coverage, D95 of gross tumor volume and planning target volume, maximum doses of tumor, and the spinal cord were compared for each plan, taking into consideration the tumor location. Results: According to the Monte Carlo calculations, mean tumor volume coverage of the 4D plans was 4.4% higher than the 3D plans when tumors were located in the lower lobes of the lung, but were 4.6% lower when tumors were located in the upper lobes of the lung. Similarly, the D95 of 4D plans was 4.8% higher than 3D plans when tumors were located in the lower lobes of lung, but was 1.7% lower when tumors were located in the upper lobes of lung. This tendency was also observed at the maximum dose of the spinal cord. Lastly, a 30% reduction in the PTV volume coverage was observed for the Monte Carlo calculation compared with the Ray-tracing calculation. Conclusion: 3D and 4D robotic radiotherapy treatment plans for lung cancers were compared according to a dosimetric viewpoint for a tumor and the spinal cord. The difference of tumor dose distributions between 3D and 4D treatment plans was only significant when large tumor movement and deformation was suspected. Therefore, 4D treatment planning is only necessary for large tumor motion and deformation. However, a Monte Carlo calculation is always necessary, independent of tumor motion in the lung.

• The Korean Journal of Applied Statistics
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• v.13 no.2
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• pp.505-514
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• 2000

A Markov Chain Monte Carlo method with data augmentation is developed to compute the features of the posterior distribution. For each observed failure epoch, we introduced mixture failure model of Rayleigh and Erlang(2) pattern. This data augmentation approach facilitates specification of the transitional measure in the Markov Chain. Gibbs steps are proposed to perform the Bayesian inference of such models. For model determination, we explored sum of relative error criterion that selects the best model. A numerical example with simulated data set is given.

• Progress in Medical Physics
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• v.14 no.4
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• pp.240-248
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• 2003

The Monte Carlo calculation is the most accurate means of predicting radiation dose, but its accuracy is accompanied by an increase in the amount of time required to produce a statistically meaningful dose distribution. In this study, the effects on calculation time by introducing variance reduction techniques and increasing computing power, respectively, in the Monte Carlo dose calculation for a 6 MV photon beam from the Varian 600 C/D were estimated when maintaining accuracy of the Monte Carlo calculation results. The EGSnrc­based BEAMnrc code was used to simulate the beam and the EGSnrc­based DOSXYZnrc code to calculate dose distributions. Variance reduction techniques in the codes were used to describe reduced­physics, and a computer cluster consisting of ten PCs was built to execute parallel computing. As a result, time was more reduced by the use of variance reduction techniques than that by the increase of computing power. Because the use of the Monte Carlo dose calculation in clinical practice is yet limited by reducing the computational time only through improvements in computing power, introduction of reduced­physics into the Monte Carlo calculation is inevitable at this point. Therefore, a more active investigation of existing or new reduced­physics approaches is required.

• Journal of the Korean Data and Information Science Society
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• v.10 no.1
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• pp.119-133
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• 1999

A Markov Chain Monte Carlo method is developed to compute the software reliability model. We consider computation problem for determining of posterior distibution in Bayseian inference. Metropolis algorithms along with Gibbs sampling are proposed to preform the Bayesian inference of the Mixed model with record value statistics. For model determiniation, we explored the prequential conditional predictive ordinate criterion that selects the best model with the largest posterior likelihood among models using all possible subsets of the component intensity functions. To relax the monotonic intensity function assumptions. A numerical example with simulated data set is given.

• The Korean Journal of Applied Statistics
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• v.14 no.2
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• pp.379-391
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• 2001

본 연구에서는 관심거리가 되고 있는 마코프인쇄 몬테칼로(Markov Chain Monte Carlo, MCMC)방법에 근거한 공간 확률난수 (spatial random variate)생성법과 깁스표본추출법(Gibbs sampling)에 의한 베이지안 분석 방법에 대한 기술적 사항들에 관하여 검토하였다. 먼저 기본적인 확률난수 생성법과 관련된 사항을 살펴보고, 다음으로 조건부명시법(conditional specification)을 이용한 공간 확률난수 생성법을 예를 들어 살펴보기로한다. 다음으로는 이렇게 생성된 공간자료를 분석하기 위하여 깁스표본추출법을 이용한 베이지안 사후분포를 구하는 방법을 살펴보았다.

• Journal of Radiation Protection and Research
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• v.40 no.1
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• pp.55-64
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• 2015

Dose calculations which are a crucial requirement for radiotherapy treatment planning systems require accuracy and rapid calculations. The conventional radiotherapy treatment planning dose algorithms are rapid but lack precision. Monte Carlo methods are time consuming but the most accurate. The new combined system that Monte Carlo methods calculate part of interesting domain and the rest is calculated by neural can calculate the dose distribution rapidly and accurately. The preliminary study showed that neural networks can map functions which contain discontinuous points and inflection points which the dose distributions in inhomogeneous media also have. Performance results between scaled conjugated gradient algorithm and Levenberg-Marquardt algorithm which are used for training the neural network with a different number of neurons were compared. Finally, the dose distributions of homogeneous phantom calculated by a commercialized treatment planning system were used as training data of the neural network. In the case of homogeneous phantom;the mean squared error of percent depth dose was 0.00214. Further works are programmed to develop the neural network model for 3-dimensinal dose calculations in homogeneous phantoms and inhomogeneous phantoms.