• 한국경영과학회지
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• 제22권1호
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• pp.75-85
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• 1997

A stable algorithm for computing the fundamental matrix (I-Q)$^{-1}$ of a Markov chain is proposed, where Q is a substochastic matrix. The proposed algorithm utilizes the GTH algorithm (Grassmann, Taskar and Heyman, 1985) which is turned out to be stable for finding the steady state distribution of a finite Markov chain. Our algorithm involves no subtractions and therefore loss of significant digits due to concellation is ruled out completely while Gaussian elimination involves subtractions and thus may lead to loss of accuracy due to cancellation. We present numerical evidence to show that our algorithm achieves higher accuracy than the ordinagy Gaussian elimination.

• International Journal of Quality Innovation
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• 제2권2호
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• pp.136-144
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• 2001

The Markov Chain approach is used to develop an economic adjustment model of a process whose quality can be affected by a single special cause, resulting in changes of the process mean by incorrect adjustment of the process when it is operating according to its capability. The $\bar{X}$ control chart is thus used to signal the special cause. It is demonstrated that the expressions for the expected cycle time and the expected cycle cost are easier to obtain by the proposed approach than by adopting that in Collani, Saniga and Weigang (1994). Furthermore, this approach would be easily extended to derive the expected cycle cost and the expected cycle time for the case of multiple special causes or multiple control charts. A numerical example illustrates the proposed method and its application.

• Journal of the Korean Statistical Society
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• 제32권4호
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• pp.401-409
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• 2003

We consider a particle walking on the nonnegative integers and each unit of time it makes, given it is at site k, either a jump of size m distance units to the right with probability $p_{k}$ or it goes back (falls down) to its starting point 0, a retaining barrier, with probability $v_{k}\;=\;1\;-\;p_{k}$. This is a Markov chain on the integers $mZ^{+}$. We show that if $v_{k}$ has a nonzero limit, then the Markov chain is positive recurrent. However, if $v_{k}$ speeds to 0, then we may get transient Markov chain. A critical speeding rate to zero is identified to get transience, null recurrence, and positive recurrence. Another type of random walk on $Z^{+}$ is considered in which a particle moves m distance units to the right or 1 distance unit to left with probabilities $p_{k}\;and\;q_{k}\;=\;1\;-\;p_{k}$, respectively. A necessary condition to having a stationary distribution and positive recurrence is obtained.

• 응용통계연구
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• 제25권5호
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• pp.837-846
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• 2012

Monte Carlo methods have been used in exact inference for contingency tables for a long time; however, they suffer from ergodicity and the ability to achieve a desired proportion of valid tables. In this paper, we apply the stochastic approximation Monte Carlo(SAMC; Liang et al., 2007) algorithm, as an adaptive Markov chain Monte Carlo, to the exact test of mutual independence in a multiway contingency table. The performance of SAMC has been investigated on real datasets compared to with existing Markov chain Monte Carlo methods. The numerical results are in favor of the new method in terms of the quality of estimates.

• Communications for Statistical Applications and Methods
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• 제27권5호
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• pp.569-578
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• 2020

Various graph clustering methods have been introduced to identify communities in social or biological networks. This paper studies the entropy-based and the Markov chain-based methods in clustering the undirected graph. We examine the performance of two clustering methods with conventional methods based on quality measures of clustering. For the real applications, we collect the mathematical subject classification (MSC) codes of research papers from published mathematical databases and construct the weighted code-to-document matrix for applying graph clustering methods. We pursue to group MSC codes into the same cluster if the corresponding MSC codes appear in many papers simultaneously. We compare the MSC clustering results based on the several assessment measures and conclude that the Markov chain-based method is suitable for clustering the MSC codes.

• 통합자연과학논문집
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• 제1권2호
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• pp.127-132
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• 2008

This project follows the heterogeneous agent market segmented model of Landon-Lane and Occhino (2007) with using Korean data, M1 and GDP deflator from 1882:I to 2007:II. This paper estimates parameters with Monte Carlo Markov Chain. The fraction of traders, ${\lambda}$, in Korea is 15.64%. The quarterly preferences discount factor's, ${\beta}$, posterior mean is 0.9922. The posterior mean of the inverse of the elasticity of the labor supply to the real wage, ${\varphi}$, is 0.0316. The elasticity of the labor supply to the real wage has a very large value. By Hansen (1985) and Christiano and Eichenbaum (1992) and Cooley and Hansen (1989), models having large elasticity of the aggregate labor supply better match macroeconomic data.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2010년도 학술발표회
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• pp.1495-1499
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• 2010

최근에 기후변화 영향 분석을 위한 강수모의발생 기법에 대한 연구가 중요한 문제로 대두되고 있다. 기본적으로 모의된 강수량이 유역단위에서 의미 있는 값으로 수문모형에 입력자료로 활용되기 위해서는 강수지점간의 공간상관성의 유지가 매우 중요하다. 즉 지역적인 수문학적 거동을 유역단위에서 평가하기 위해서는 유역상관성을 고려할 수 있는 다지점(multisite) 모형의 개발이 필수적이다. 이러한 점에서 본 연구에서는 다지점 강수모의기법을 개발하였으며 비정상성 해석이 가능하도록 동역학적 강수모형을 구성하였다. 이를 한강유역 강수지점에 적용하여 모형의 적합성을 평가하였다.

• 대한산업공학회지
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• 제42권2호
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• pp.86-95
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• 2016

We propose a new approach to the stochastic version of Lanchester model. Commonly used approach to stochastic Lanchester model is through the Markov-chain method. The Markov-chain approach, however, is not appropriate to high dimensional heterogeneous force case because of large computational cost. In this paper, we propose an approximation method of stochastic Lanchester model. By matching the first and the second moments, the distribution of each unit strength can be approximated with multivariate normal distribution. We evaluate an approximation of discrete Markov-chain model by measuring Kullback-Leibler divergence. We confirmed high accuracy of approximation method, and also the accuracy and low computational cost are maintained under high dimensional heterogeneous force case.

• Communications for Statistical Applications and Methods
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• 제17권3호
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• pp.441-450
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• 2010

In this paper we consider the problem of forecasting binomial time series, modelled by the binomial autoregressive model. This paper considers proposed by McKenzie (1985) and is extended to a higher order by $Wei{\ss}$(2009). Since the binomial autoregressive model is a Markov chain, we can apply the earlier work of Bu and McCabe (2008) for integer valued autoregressive(INAR) model to the binomial autoregressive model. We will discuss how to compute the h-step-ahead forecast of the conditional probabilities of $X_{T+h}$ when T periods are used in fitting. Then we obtain the maximum likelihood estimator of binomial autoregressive model and use it to derive the maximum likelihood estimator of the h-step-ahead forecast of the conditional probabilities of $X_{T+h}$. The methodology is illustrated by applying it to a data set previously analyzed by $Wei{\ss}$(2009).

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제8권9호
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• pp.3110-3125
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• 2014

Network coding improves TCP's performance in lossy wireless networks. However, the complex congestion window evolution of network coded TCP (TCP-NC) makes the analysis of end-to-end throughput challenging. This paper analyzes the evolutionary process of TCP-NC against lossy links. An analytic model is established by applying a two-dimensional Markov chain. With maximum window size, end-to-end erasure rate and redundancy parameter as input parameters, the analytic model can reflect window evolution and calculate end-to-end throughput of TCP-NC precisely. The key point of our model is that by the novel definition of the states of Markov chain, both the number of related states and the computation complexity are substantially reduced. Our work helps to understand the factors that affect TCP-NC's performance and lay the foundation of its optimization. Extensive simulations on NS2 show that the analytic model features fairly high accuracy.