• Journal of the Korean Statistical Society
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• v.35 no.3
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• pp.251-260
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• 2006

The proportional hazards model (PHM) can be associated with a non- homogeneous Markov chain (NHMC) in the sense that sample alignments in the PHM correspond to trajectories of the NHMC. As a result the partial likelihood widely used for the PHM is a probabilistic function of the trajectories of the NHMC. In this paper, we show that, as the total number of subjects involved increases, the trajectories of the NHMC, i.e. sample alignments in the PHM, converges to the solution of an ordinary differential equation which, subsequently, characterizes the almost sure limit of the partial likelihood.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.37 no.1B
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• pp.50-58
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• 2012

The objective of this study is to develop the theoretical model of the telecommunication system service availability from the user perspective. We assume non-homogeneous Poisson process for the call arrival process and continuous time Markov chain for the system state. The proposed model effectively describes the user model of the user-perceived service reliability by including the time-varying call arrival rate. We also include the operational failure state where the user cannot receive any service even though the system is functioning.

• Communications for Statistical Applications and Methods
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• v.21 no.2
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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.

• Management Science and Financial Engineering
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• v.12 no.2
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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.

• Computers and Concrete
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• v.18 no.1
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• pp.69-97
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• 2016

Performance-based remaining life assessment of reinforced concrete bridge girders, subject to chloride-induced corrosion of reinforcement, is addressed in this paper. Towards this, a methodology that takes into consideration the human judgmental aspects in expert decision making regarding condition state assessment is proposed. The condition of the bridge girder is specified by the assignment of a condition state from a set of predefined condition states, considering both serviceability- and ultimate- limit states, and, the performance of the bridge girder is described using performability measure. A non-homogeneous Markov chain is used for modelling the stochastic evolution of condition state of the bridge girder with time. The thinking process of the expert in condition state assessment is modelled within a probabilistic framework using Brunswikian theory and probabilistic mental models. The remaining life is determined as the time over which the performance of the girder is above the required performance level. The usefulness of the methodology is illustrated through the remaining life assessment of a reinforced concrete T-beam bridge girder.

• 한국방재학회:학술대회논문집
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• 2008.02a
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• pp.501-504
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• 2008

A non-homogeneous markov model which is able to simulate hourly rainfall series is developed for estimating reliable hydrological variables. The proposed approach is applied to simulate hourly rainfall series in Korea. The simulated rainfall is used to estimate the design rainfall and compared to observations in terms of reproducing underlying distributions of the data to assure model's validation. The model shows that the simulated rainfall series reproduce a similar statistical attribute with observations, and expecially maximum value is gradually increased as number of simulation increase.

• The Korean Journal of Applied Statistics
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• v.27 no.2
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• pp.263-275
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• 2014

The present study used a hierarchical Bayesian approach was used to develop a mixed effect model to describe the transitional behavior of subjects in time nonhomogeneous Markov chains. The posterior distributions of model parameters were not in analytically tractable forms; subsequently, a Gibbs sampling method was used to draw samples from full conditional posterior distributions. The proposed model was implemented with real data.

• Journal of Korea Water Resources Association
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• v.41 no.3
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• pp.251-264
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• 2008

In this study, a nonhomogeneous markov model which is able to simulate hourly rainfall series is developed for estimating reliable hydrologic variables. The proposed approach is applied to simulate hourly rainfall series in Korea. The simulated rainfall is used to estimate the design rainfall and flood in the watershed, and compared to observations in terms of reproducing underlying distributions of the data to assure model's validation. The model shows that the simulated rainfall series reproduce a similar statistical attribute with observations, and expecially maximum value is gradually increased as number of simulation increase. Therefore, with the proposed approach, the non-homogeneous markov model can be used to estimate variables for the purpose of design of hydraulic structures and analyze uncertainties associated with rainfall input in the hydrologic models.

• Journal of Korea Water Resources Association
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• v.52 no.8
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• pp.545-554
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• 2019

The most drought assessments are based on a drought index, which depends on univariate variables such as precipitation and soil moisture. However, there is a limitation in representing the drought conditions with single variables due to their complexity. It has been acknowledged that a multivariate drought index can more effectively describe the complex drought state. In this context, this study propose a Copula-based drought index that can jointly consider precipitation and soil moisture. Unlike precipitation data, long-term soil moisture data is not readily available so that this study utilized a Gaussian Mixture Non-Homogeneous Hidden Markov chain Model (GM-NHMM) model to simulate the soil moisture using the observed precipitation and temperature ranging from 1973 to 2014. The GM-NHMM model showed a better performance in terms of reproducing key statistics of soil moisture, compared to a multiple regression model. Finally, a bivariate frequency analysis was performed for the drought duration and severity, and it was confirmed that the recent droughts over Jeollabuk-do in 2015 have a 20-year return period.