• Management Science and Financial Engineering
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• 제12권2호
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• pp.19-35
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• 2006

We use the hierarchical Bayesian approach to describe the transition probabilities of a binary nonhomogeneous Markov chain. The Markov chain is used for describing the transition behavior of emotionally disturbed children in a treatment program. The effects of covariates on transition probabilities are assessed using a logit link function. To describe the time evolution of transition probabilities, we consider two modeling strategies. The first strategy is based on the concept of exchangeabiligy, whereas the second one is based on a first order Markov property. The deviance information criterion (DIC) measure is used to compare models with two different time dependent structures. The inferences are made using the Markov chain Monte Carlo technique. The developed methodology is applied to some real data.

• Structural Engineering and Mechanics
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• 제81권1호
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• pp.103-115
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• 2022

The prediction error variances for frequencies are usually considered as unknown in the Bayesian system identification process. However, the error variances for mode shapes are taken as known to reduce the dimension of an identification problem. The present study attempts to explore the effectiveness of Bayesian approach of model parameters updating using Markov Chain Monte Carlo (MCMC) technique considering the prediction error variances for both the frequencies and mode shapes. To remove the ergodicity of Markov Chain, the posterior distribution is obtained by Gaussian Random walk over the proposal distribution. The prior distributions of prediction error variances of modal evidences are implemented through inverse gamma distribution to assess the effectiveness of estimation of posterior values of model parameters. The issue of incomplete data that makes the problem ill-conditioned and the associated singularity problem is prudently dealt in by adopting a regularization technique. The proposed approach is demonstrated numerically by considering an eight-storey frame model with both complete and incomplete modal data sets. Further, to study the effectiveness of the proposed approach, a comparative study with regard to accuracy and computational efficacy of the proposed approach is made with the Sequential Monte Carlo approach of model parameter updating.

• 응용통계연구
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• 제24권4호
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• pp.657-676
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• 2011

통계적 공정관리절차의 특성은 해석적 해를 얻기가 어려운 경우가 많이 있으나 Markov연쇄를 적용하면 가능한 경우가 많이 있다. 이 논문에서는 공정 통계량이 Markov특성을 따르는 경우, Markov연쇄를 생성하는 방법과 이를 이용한 공정관리 절차의 특성을 도출하는 방법에 대해 설명하고 있다. 관리도의 통계적 설계, 경제적 설계 및 변량 표본 추출비 설계 등의 특성 규명을 위한 Markov연쇄의 적용에 대한 기존의 알려진 방법을 복습하고 또한 새로운 공정관리 분야인 재조정 관리도에의 적용방법에 대한 연구결과도 보여주고 있다. 공정관리의 특성연구에서 해석적 해가 가능한 경우에도 이 과정이 복잡하여 Markov연쇄를 병행 사용하면 특성 규명이 명확해지며, 모의실험보다는 짧은 시간에 더 정밀한 결과를 얻을 수 있어 널리 이용되고 있다.

• 응용통계연구
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• 제34권4호
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• pp.537-556
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• 2021

통계적 공정관리절차의 특성은 해석적 해를 얻기가 어려운 경우가 많이 있으나 Markov연쇄를 적용하면 가능한 경우가 많이 있다. 이 논문에서는 공정 통계량이 Markov특성을 따르는 경우, Markov연쇄를 생성하는 방법과 이를 이용한 공정관리 절차의 특성을 도출하는 방법에 대해 설명하고 있다. 관리도의 통계적 설계, 경제적 설계 및 변량표본 추출비 설계 등의 특성 규명을 위한 Markov연쇄의 적용에 대한 기존의 알려진 방법을 복습하고 또한 새로운 공정관리 분야인 재조정 관리도에의 적용방법에 대한 연구결과도 보여주고 있다. 공정관리의 특성연구에서 해석적 해가 가능한 경우에도 이 과정이 복잡하여 Markov연쇄를 병행 사용하면 특성 규명이 명확해지며, 모의실험보다는 짧은 시간에 더 정밀한 결과를 얻을 수 있어 널리 이용되고 있다.

• 대한토목학회논문집
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• 제33권5호
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• pp.1861-1870
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• 2013

최근 기후변화 영향으로 인해 수문변동성이 크게 증가되고 있으며 이러한 변동성을 고려하기 위한 방안으로서 강수량 모의발생 기법에 대한 중요성이 대두되고 있다. 본 연구에서는 복잡한 강수발생 패턴을 인지하고 강수량의 다양한 분포특성을 고려할 수 있는 혼합분포를 이용한 동질성 Hidden Markov Chain(HMM) 모형을 제안하였다. HMM 모형의 개선효과를 검증하기 위해서 기존 Markov Chain 모형과 비교 하였으며 서울관측소 및 전주관측소를 대상으로 연구를 진행하였다. 계절강수량 및 일강수량 등 다양한 시간규모에서 모형의 적합성을 평가하기 위해서 천이확률, 평균, 분산, 왜곡도 및 첨예도 등을 비교하였으며 HMM 모형이 기존 Markov Chain 모형에 비해서 개선된 모의능력을 확인할 수 있었다. 특히, HMM 모형은 극치강수량을 재현하는데 있어서 기존 Markov Chain 모형에 비해서 월등한 모의능력을 보여주었다. 이러한 점에서 장기유출량 및 확률홍수량 등을 산정하기 위한 입력자료로 활용이 충분히 가능할 것으로 판단된다.

• 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.

• 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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• 제21권2호
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• pp.135-145
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• 2014

The present study surveys Bayesian modeling structure for inferences about transition probabilities of Markov chain. The motivation of the study came from the data that shows transitional behaviors of emotionally disturbed children undergoing residential treatment program. Dirichlet distribution was used as prior for the multinomial distribution. The analysis with real data was implemented in WinBUGS programming environment. The performance of the model was compared to that of alternative approaches.

• ETRI Journal
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• 제39권5호
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• pp.718-728
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• 2017

Empirical modeling of wireless fading channels using common schemes such as autoregression and the finite state Markov chain (FSMC) is investigated. The conceptual background of both channel structures and the establishment of their mutual dependence in a confined manner are presented. The novel contribution lies in the proposal of a new approach for deriving the state transition probabilities borrowed from economic disciplines, which has not been studied so far with respect to the modeling of FSMC wireless fading channels. The proposed approach is based on equal portioning of the received signal-to-noise ratio, realized by using an alternative probability construction that was initially highlighted by Tauchen. The associated statistical procedure shows that a first-order FSMC with a limited number of channel states can satisfactorily approximate fading. The computational overheads of the proposed technique are analyzed and proven to be less demanding compared to the conventional FSMC approach based on the level crossing rate. Simulations confirm the analytical results and promising performance of the new channel model based on the Tauchen approach without extra complexity costs.

• 통합자연과학논문집
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• 제7권3호
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• pp.200-207
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• 2014

Average number of samples to signal (ANSS) and average time to signal (ATS) are the most widely used criterion for comparing the efficiencies of the quality control charts. In this study the method of evaluating ANSS and ATS values of the multivariate exponentially weighted moving average (EWMA) control charts with Markov chain approach was presented when the production process is in control state or out of control state. Through numerical results, it is found that when the number of transient state r is less than 50, the calculated ANSS and ATS values are unstable; and ATS(r) tends to be stabilized when r is greater than 100; in addition, when the properties of multivariate EWMA control chart is evaluated using Markov chain method, the number of transient state r requires bigger values when the smoothing constatnt ${\lambda}$ becomes smaller.