Assessment of Using Statistical Leakage Estimation at the Macro Level for VLSI Designs

Jae Hoon Kim,Wook Kim,Young Hwan Kim 대한전자공학회 2009 ITC-CSCC :International Technical Conference on Ci Vol.2009 No.7

With the rapid increase of process variation, the necessity of high-level statistical analysis that considers the performance variation of circuit components is being emphasized today. However, while most work on statistical leakage estimation has focused on gate-level design, its use for high-level design has not been well established yet. This paper assesses the effectiveness of using statistical leakage estimation for high-level design through the extensive comparison of the worst-case leakage estimation results with those of the statistical leakage estimation.

산림의 지역적 특성을 고려한 시군구 임목축적량 통계 산출 기법 개발

김은숙 ( Eun Sook Kim ),김철민 ( Cheol Min Kim ) 한국산림과학회 2015 한국산림과학회지 Vol.104 No.1

Forest statistics of local administrative districts have many social needs, nevertheless we have some difficulties for working out an accurate statistics because of insufficient data in small-area level. Thus, new small-area estimation method has to set aside additional data, decrease errors of statistics and consider the local forest characteristics at the same time. In this study, we researched the spatial divisions that can set aside additional data for statistics production and satisfy the major premise, which is “forest characteristics of spatial divisions have to be equal to that of small-area”. And we compared synthetic estimation methods based on three different spatial divisions(provinces, neighbor districts and new expanded districts). New expanded districts were divided based on the criteria of climate, soil type and tree species composition that affects local forest characteristics. Small-area statistics were assessed in terms of the ability to estimate local forest characteristics and consistency within large-area statistics. As a result, new expanded districts synthetic estimation was assessed to calculate statistics that reflects local forest characteristics better than other two estimation methods. Moreover, this synthetic estimation method produced the statistics that was included within 95% confidence interval of large-area statistics and was the closer to large-area statistics than the neighbor districts synthetic estimation.

통계적 추정을 가르치기 위한 수학적 지식(MKT)의 분석

최민정 ( Choi Min Jeong ),이종학 ( Lee Jong Hak ),김원경 ( Kim Won Kyung ) 한국수학교육학회 2016 수학교육 Vol.55 No.3

Knowledge and data interpretation on statistical estimation was important to have statistical literacy that current curriculum was said not to satisfy. The author investigated mathematics teachers`` MKT on statistical estimation concerning interpretation of confidence interval by using questionnaire and interview. SMK of teachers`` confidence was limited to the area of textbooks to be difficult to interpret data of real life context. Most of teachers wrongly understood SMK of interpretation of confidence interval to have influence upon PCK making correction of students`` wrong concept. SMK of samples and sampling distribution that were basic concept of reliability and confidence interval cognized representation of samples rather exactly not to understand importance and value of not only variability but also size of the sample exactly, and not to cognize appropriateness and needs of each stage from sampling to confidence interval estimation to have great difficulty at proper teaching of statistical estimation. PCK that had teaching method had problem of a lot of misconception. MKT of sample and sampling distribution that interpreted confidence interval had almost no relation with teachers`` experience to require opportunity for development of teacher professionalism. Therefore, teachers were asked to estimate statistic and to get confidence interval and to understand concept of the sample and think much of not only relationship of each concept but also validity of estimated values, and to have knowledge enough to interpret data of real life contexts, and to think and discuss students`` concepts. So, textbooks should introduce actual concepts at real life context to make use of exact orthography and to let teachers be reeducated for development of professionalism.

고등학교 <확률과 통계>의 통계적 추정 단원 재구조화 방안 탐색

이송희,이경화,김하림 대한수학교육학회 2023 수학교육학연구 Vol.33 No.2

This study aimed to improve statistical estimation teaching practices in school mathematics, support the development of textbooks according to the 2022 revised mathematics curriculum, and the implementation of the curriculum in the schools. Apropos this, the directions of restructuring the statistical estimation unit were derived by synthesizing the results of previous studies related to statistical estimation. Based on these, specific restructuring suggestions for the statistical estimation unit are proposed as follows. First, in relation to the meaning of the sample and sampling method, it is necessary to focus on the bias in the sampling process to promote conceptual understanding in terms of sample representativeness and to promote the recognition of sampling variability using technologies. Second, in relation to sampling distribution, it is necessary to construct contents that promote conceptual understanding of sampling distribution and the relationship between sample size and sampling variability using simulation. Third, in relation to the confidence interval, it is necessary to construct contents that promote the recognition of the confidence levels as probabilistic confidence and provide interpretation and evaluation opportunities of estimation results using sampling errors. In addition, some examples from foreign mathematics textbooks, that can be referred to when implementing each restructuring suggestion, are explored and presented. 본 연구에서는 학교 수학에서의 통계적 추정 지도 관행을 개선하고 2022 개정 수학과 교육과정에 따른 교과서 개발 및 학교현장에서의 교육과정 실행을 지원하고자 하였다. 이를 위해 통계적 추정과 관련하여 이루어진 선행연구 결과와 2022 개정 수학과교육과정의 관련 내용을 종합하여 통계적 추정 단원의 재구조화 방향을 도출하였다. 이를 토대로 통계적 추정 단원의 구체적인재구조화 방안을 다음과 같이 제안하였다. 첫째, 표본의 뜻, 표본추출 방법과 관련하여 표본추출 과정에서 편향에 주목하게하여 표본대표성 측면에서 개념적 이해를 촉진하고, 공학 도구를 활용하여 표집변이성의 인식을 촉진하는 내용을 구성한다. 둘째, 표집분포와 관련하여 시뮬레이션을 활용하여 표집분포에 대한 개념적 이해 및 표본의 크기와 표집변이성 사이의 관계에대한 이해를 촉진하는 내용을 구성한다. 셋째, 신뢰구간과 관련하여 확률적 자신감으로서 신뢰수준을 인식하도록 촉진하고, 표본오차를 활용하여 추정 결과의 해석 및 평가 기회를 제공하는 내용을 구성한다. 또한, 각각의 재구조화 방안을 구현할 때참고할 수 있는 국외 수학 교과서의 사례를 탐색하여 제시하였다.

신뢰성 시험 평가를 위한 통계적 시료수 결정에 대한 연구

김승현(Seung-Hyun Kim),염종섭(Jongseop Yeom),백일섭(Il-Seob Baek),김종선(Jong-Sun Kim),성시일(Si-Il Sung) 한국신뢰성학회 2020 신뢰성응용연구 Vol.20 No.1

Purpose: Determineing the sample size based on a statistical theory is regarded as a quantitative, effective, and rational method, but applying it in practice is difficult. Therefore, we treat a rule for determining the sample size by considering its practical applicability to real datasets. Methods: We examined sampling-based and parameter estimation-based statistical approaches. For the sampling-based approach, we dealt with the statistical theories and derivation processes and examined their interrelationships. For the parameter estimation-based approach, we treated the principle of sample size by considering the precision of the mean and interval estimation. Results: We treated the statistical theories and derivations of the various approaches and dealt with their interrelationships for methods to determine the sample size. Conclusion: From the various reliability test perspectives at the product development stage, the sampling-based approach can be applied to durability, environmental, and lifetime testing, while the parameter estimation-based approach can be used for the performance testing.

동영상 부호화의 움직임 추정 및 보상을 위한 고속 다중 참조 프레임 선택 기법

김재훈(Jae-Hoon Kim),김명진(Myoung-Jin Kim),홍민철(Min-Cheol Hong) 한국통신학회 2007 韓國通信學會論文誌 Vol.32 No.11C

본 논문에서는 동영상 부호화 방식의 움직임 추정을 위한 고속 다중 참조 프레임 선택 기법에 대해 제안한다. 움직임 추정을 위해 다중 프레임을 참조하는 H.264 동영상 부호화 방식의 경우, 블록별로 선택된 최적의 참조 프레임들은 일정한 상관관계를 유지하는 특성이 존재한다. 제안 방식은 이러한 통계적 특성을 이용하여, 임의의 블록 크기의 움직임 추정 모드에서 선택된 최적의 참조 프레임 정보를 이용하여 하위 블록 크기의 움직임 추정 모드에서 사용할 참조 프레임을 예측한다. 실험 결과를 통해 5개의 참조 프레임 사용을 기준으로 제안하는 기법을 사용하였을 때, 움직임 추정에 소요되는 시간은 가용한 모든 참조 프레임에 대해 움직임 추정을 수행하는 방식 대비 평균 60% 감소되었으며, PSNR 및 발생 비트율 측면에서 거의 동일한 성능을 유지함을 확인할 수 있었다. In this paper, we propose a fast multiple reference frame selection method for motion estimation and compensation in video coding. Reference frames selected as an optimal reference frame by variable block sizes motion estimation have the statistical characteristic that was based on block size. Using the statistical characteristic, reference frames for smaller block size motion estimation can be selected from reference frame which was decided as an optimal one for the upper layer block size. Simulation results show that the proposal method decreased the computations about 60%. Nevertheless, PSNR and bit rate were almost same as the performances of original H.264 multiple reference motion estimation.

Image visualization of photon counting confocal microscopy using statistical estimation

Jang, J.Y.,Cho, M. Wissenschaftliche Verlagsgesellschaft m. b. H 2016 OPTIK -STUTTGART- Vol.127 No.2

<P>In this paper, we propose image visualization method of photon counting confocal microscopy using statistical estimation. Since high power coherent light source is used to record sectional images from micro-objects in conventional confocal microscopy, it may cause damage for a structure of micro-objects. Thus, low power coherent light source may be required. However, in low light level environment, it is difficult to capture sectional images of micro-objects. On the other hand, photon counting imaging technique can detect sectional images of micro-objects in photon-starved conditions. Therefore, in this paper, we apply a photon counting imaging technique to conventional confocal microscopy for visualization of micro-objects. Photon counting detection can be modeled by statistical process. To visualize micro objects under photon-starved conditions, statistical estimation methods such as maximum likelihood estimation can be used. In addition, we present color photon counting imaging system which considers different carried photon energy with each basic color channels. To prove and evaluate our method, we show simulation results for image visualization of photon counting confocal microscopy and calculate mean square error. (C) 2015 Elsevier GmbH. All rights reserved.</P>

실무연구(實務硏究) : 법과 통계의 만남 -담합으로 인한 손해액의 통계적 추정-

이준석 ( Joon Seok Lee ) 법조협회 2015 法曹 Vol.64 No.4

가격담합으로 인한 손해배상청구 소송의 경우, 그 손해액을 산정함에 있어서 계량 경제학적 방법론이 널리 사용되고 있다. 하지만 이를 이해하는 데에는 법 外적인 전문성이 요구되기에, 법률가들은 경제학자 등 외부 전문가들의 감정 등에 의존하고자 한다. 문제는 외부 전문가들 사이에서도 손해액에 대한 견해 차이가 상당하다는 점이다. 그리고 많은 계량경제학적 쟁점들이 최종적으로 법적 판단에 의하게 되는 손해액 산정과 긴밀히 연결되어 있어, 어느 부분은 법적 판단 영역이고 어느 부분은 외부 전문가에게 맡기면 되는 사실 판단 영역인지 그 구별이 매우 어렵다. 따라서 법률가들의 이에 대한 이해는 불가피하다. 그럼에도 그동안의 선행연구들은 구체적으로 어떠한 형태의 계량경제학적 회귀모형을 법원이 채택해야 할 것인지, 가령 어떤 변수를 추가한 혹은 제거한 모형이 좀 더 타당한지, 각 모형에 대하여 어느 정도의 통계적 유의수준을 요구해야 할 것인지 등의 쟁점에 관하여는 자세히 다루지 않았다. 따라서 본 논문에서는 위 쟁점들을 다루고자하며, 그 과정에서 한국과 미국의 관련 판례 및 학계의 논의를 검토 및 소개함으로써, 한국 현실에의 시사점을 얻고자 한다. Many legal professionals are having a hard time figuring out what should be an appropriate amount of damage in a price-fixing case. Estimating damage is difficult since statistics is widely used during the process in order to measure the hypothetical competitive price, which is essential in determining the amount of damage. But judges and lawyers do not have much prior knowledge on statistics. Therefore, they cannot help but relying on expert witnesses who specialize in that field. Most of the time, however, experts also disagree over the adequate amount of damage. Recently there was a court case in South Korea, where expert witnesses of both sides differed in their damage estimates, the gap between them even reaching 100 billion KRW. Thus legal professionals cannot shun from statistical debates if they want to solve this ‘legal’ dispute. Previous literature in the legal studies did not touch upon this issue thoroughly where both statistics and the law are pertinent. This paper tries to fill in the gap, especially with respect to how legal professionals should deal with various methodological issues raised by econometrical inferences. In doing so, the validity of many arguments raised at previous court cases of South Korea and the United States are discussed. For example, the defendants(South Korean oil companies) raised the argument at the recent oil price-fixing case that the coefficient of a variable, estimating the effect of price-fixing in a particular year, could not be used since it was not statistically significant with 95% confidence level. But the Seoul Central District Court(the court of 1st instance) and Seoul High Court of Justice(the court of 2nd instance) ruled against the defendants, holding that the use of that variable is permitted on the ground that the purpose of the statistical analysis of the court-appointed expert was to estimate the amount of damage, rather than to test the hypothesis of whether there was a price-fixing. This paper argues that courts`` decisions were reasonable in that 5% significance level is just a rule of thumb among social scientists, so it cannot be that a hypothesis failing to meet 5% significance level is worthless. If a coefficient is statistically significant not with 5% significance level, but with 10% significance level, for instance, it is true that the information is of slightly lower value than that satisfies 5% significance level, but it is still a useful information and the disparity between two are not large.

Generalized Anisotropic Sparse Grid Integrals Based on Adaptive High Dimension Model Representation for Moment Estimation

Zhengliang Li,Wenliang Fan,Runyu Liu,Xiangqian Sheng 대한토목학회 2021 KSCE JOURNAL OF CIVIL ENGINEERING Vol.25 No.12

Estimation of statistical moments of structural response effectively and accurately is still one of the main topics for analysis of random systems. For the sake of reducing function evaluations to alleviate curse of dimensionality and improve the accuracy in moment estimation, a generalized anisotropic sparse grid integral based on the adaptive high dimensional model representation and appropriate reference variables is proposed. By introducing different transformations, a system with general variables is transformed into the one with appropriate independent reference variables and a generalized anisotropic sparse grid integral will be presented for moment estimation. Then, anisotropic sparse grid collections should be divided into several mutually exclusive sub-collections and the generalized anisotropic sparse grid integral (SGI) can be remodeled in a new form. With this new form, the adaptive high dimensional model representation can be introduced for function evaluations conveniently, which can be regarded as an alternative way to evaluate functions precisely and efficiently without any approximation. Finally, several examples are presented to demonstrate the effectiveness and accuracy of the proposed method.

와이블분포 기반 관측중단데이터에서의 베이지안 기법 및 전통적 기법 간 신뢰도 추정 기법 성능 비교

조형준(Hyoung Jun Cho),윤연아(Yeon Ah Yoon),장태우(Tai-Woo Chang),김용수(Yong Soo Kim) 한국신뢰성학회 2020 신뢰성응용연구 Vol.20 No.3

Purpose: This paper reports on the corresponding guidelines to help users select a suitable estimation method. The guidelines were derived by evaluating the reliability estimation performance of different estimation methods. Methods: Weibull distribution parameters were calculated using the least squares and maximum likelihood estimators, aling with the Bayesian methods. The scale and shape parameters were estimated to calculate the life-time. Finally, the analysis of variance was performed to compare the accuracy of the various methods. Results: Bayesian methods, which employed prior information, exhibited a relatively high performance for all sample sizes. As the sample size increased, the performance was similar to that of the least squares and maximum likelihood estimators. The performance of the Bayesian methods fluctuated according to the prior information. Conclusion: The reliability of various methods to analyze Weibull-distribution-based censoring data was analyzed. The results can be used in reliability assessment, to achieve the target reliability in the product development phase.