• Journal of the Korean Data and Information Science Society
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• 제28권1호
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• pp.153-161
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• 2017

전염병 확산에 대한 확률과정모형으로 활용되는 분기과정은 실제 데이터를 통해 모수를 추정할 수 있다는 장점이 있다. 음이항 분포를 분기과정의 생산 분포 모형으로 적용할 수 있는데 음이항 분포를 적용하기 위해서는 평균과 산포 모수를 추정하여야한다. 기존의 생물학 연구와 역학 연구 분야에서는 이를 최대우도법을 이용하여 추정하고 있다. 그러나 대부분의 역학 자료의 특성상 분기과정에서 이용되는 음이항 분포는 소표본이어서 최대우도 추정량의 정도를 충족시킬 수 없다. 본 논문에서는 소표본 자료에서 좋은 통계량의 성질을 만족한다고 알려져 있는 베이지안을 이용하여 모수를 추정하는 방법을 제안한다. 2015년 국내 메르스 사례에 베이지안 방법을 적용하여 모수를 추정하고 사후 분포를 적합하였다. 그 결과 어떠한 사전 분포를 가정하더라도 안정적으로 모수를 추정하는 것을 알 수 있었다. 추정된 산포 모수를 이용하여 분기과정에서의 전염병 소멸 확률을 유도하였다.

• 대한수학회지
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• 제38권1호
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• pp.25-35
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• 2001

In this paper we consider an age dependent branching process whose particles move according to a Markov process with continuous state space. The Markov process is assumed to the stationary with independent increments and positive recurrent. We find some sufficient conditions for he Markov motion process such that the empirical distribution of the positions converges to the limiting distribution of the motion process.

• 대한수학회지
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• 제36권6호
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• pp.1115-1132
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• 1999

We consider a supercritical multitype age dependent branching process. We define a stochastic process Zf(t) which is a functional of the empirical age distribution. When the limit of the expectation of this functional vanishes we4 find some sufficient conditions for the asymptotic normality of the mean of f with respect to the empirical age distribution at time t.

• Journal of applied mathematics & informatics
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• 제14권1_2호
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• pp.157-172
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• 2004

An age-dependent branching process where disasters occur as a renewal process leading to annihilation or survival of all the cells, is considered. For such a process, the total mean sojourn time of all the cells in the system is analysed using the regeneration point technique. The mean number of cells which die in time t and its asymptotic behaviour are discussed. When the disasters arrival as a Poisson process and the lifetime of the cells follows exponential distribution, elegant inter- relationships are found among the means of (i) the total number of cells which die in time t (ii) the total sojourn time of all cells in the system upto time t and (iii) the number of living cells at time t. Some of the existing results are deduced as special cases for related processes.

• Communications for Statistical Applications and Methods
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• 제18권6호
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• pp.809-816
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• 2011

A tree-indexed autoregressive(AR) process is a time series defined on a tree which is generated by a branching process and/or a deterministic splitting mechanism. This short article is concerned with conditional heteroscedastic structure of the tree-indexed AR models. It has been usual in the literature to analyze conditional mean structure (rather than conditional variance) of tree-indexed AR models. This article pursues to identify quadratic conditional heteroscedasticity inherent in various tree-indexed AR models in a unified way, and thus providing some perspectives to the future works in this area. The identical conditional variance of sisters sharing the same mother will be referred to as the branching heteroscedasticity(BH, for short). A quasilikelihood but preliminary estimation of the quadratic BH is discussed and relevant limit distributions are derived.

• Journal of the Korean Data and Information Science Society
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• 제25권5호
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• pp.1137-1149
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• 2014

Since the bifurcating autoregressive (BAR) model was developed by Cowan and Staudte (1986) to analyze cell lineage data, a lot of research has been directed to BAR and its generalizations. Based mainly on the author's works, this paper is concerned with a contemporary review on the BAR in terms of an overview and perspectives. Specifically, bifurcating structure is extended to multi-cast tree and to branching tree structure. The AR(1) time series model of Cowan and Staudte (1986) is generalized to tree structured random processes. Branching correlations between individuals sharing the same parent are introduced and discussed. Various methods for estimating parameters and related asymptotics are also reviewed. Consequently, the paper aims to give a contemporary overview on the BAR model, providing some perspectives to the future works in this area.

• 한국수학교육학회지시리즈A:수학교육
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• 제27권1호
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• pp.55-60
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• 1988

• 대한수학회지
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• 제36권1호
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• pp.139-157
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• 1999

Consider a supercritical Bellman-Harris process evolving from one particle. We superimpose on this process the additional structure of movement. A particle whose parent was at x at its time of birth moves until it dies according to a given Markov process X starting at x. The motions of different particles are assumed independent. In this paper we show that when the movement process X is standard Brownian the proportion of particles with position $\leq${{{{ SQRT { t} }}}} b and age$\leq$a tends with probability 1 to A(a)$\Phi$(b) where A(.) and $\Phi$(.) are the stable age distribution and standard normal distribution, respectively. We also extend this result to the case when the movement process is a Levy process.

• 한국콘텐츠학회논문지
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• 제11권8호
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• pp.475-487
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• 2011

본 논문에서는 고차원펄스의 스펙트럼을 유도하는 체계적인 방법을 제시하고, 이를 학습내용으로 하는 효율적인 이러닝 시스템을 설계한다. 고차원펄스의 스펙트럼은 연속미분법이나 콘볼루션법 등 기존의 방법에 의하여 유도될 수 있으나, 그 차수가 증가함에 따라 현저하게 높아지는 복잡도 때문에 사용할 수 없다. 우리는 고차원펄스의 차수에 따라 순환적으로 적용되는 알고리듬을 제시하고, 이를 찾아보기표에 의하여 함수적으로 차수에 연관된 스펙트럼의 식을 유도한다. 또한, 이를 이용하여 고차원펄스의 스펙트럼을 분석하는 과정을 학습하는 이러닝 콘텐츠를 설계한다. 여기에는 기존의 순차적 재생을 기본으로 하여 이른바 개념단위 오브젝트별 분기방식을 적용하는 콘텐츠 처리방식이 사용된다. 모델링, 임펄스응답과 전달함수, 파라미터, 찾아보기표 등 전체를 네 개의 개념단위로 분할한 콘텐츠페이지를 설계하고, 이들로부터 하향식으로 분화된 개념단위들을 모듈과 서브모듈로 설정한다. 이들은 개념단위 오브젝트별 분기방식에 의하여 학습자에게 다양한 학습순서와 반복학습 등을 제공하여 상호작용을 증대하고, 저작된 이러닝 콘텐츠에 의한 학습효과를 현저히 향상시킨다. 또한, 콘텐츠 자체의 효율성 측면에서도 현저한 향상을 이룬다.

• 영어영문학
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• 제56권6호
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• pp.1191-1210
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• 2010

This article claims that English liquid consonants are characterized by the presence of complex place nodes, regardless of dialectal varieties. The primary difference between rhotic and laterals can be pursued in a phonological sense. The level of subbranching nodes is in charge of the disparities among two types of liquids: the branching immediately below the Coronal node with laterals, while branching at the secondary sublevel with rhotics. In this context, the processes of rhotic deletion and lateral vocalization can be understood as those motivated to get rid of complex place nodes. That is, those processes take place as part of phonological attrition. Next, the onset/coda asymmetry regarding liquids stems from the dispreference of vocoid at the onset position, which is readily accounted for by the series of constraints on the well-formedness on the onset, namely Harmonic Onset. The rationale of gradualness and harmonic improvement proposed by Harmonic Serialism is useful to separate the attested outputs from unattested ones across the whole gamut of English varieties. All in all, the primary benefits of our analysis can be found in the consistence in the explanation for the operations running through the sounds regarded as belonging to liquid consonants, comprising the whole range of rhotic and lateral consonants.