• 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.

• Journal of the Korea Institute of Military Science and Technology
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• v.17 no.1
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• pp.41-49
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• 2014

In this paper, we consider a method to access the number of aircraft requirement which is a strategic variable in national security. This problem becomes more important considering the F-X and KF-X project in ROKAF. Traditionally, ATO(Air Tasking Order) and fighting power index have been used to evaluate the number of aircrafts required in ROKAF. However, those methods considers static aspect of aircraft requirement. This paper deals with a model to accommodate dynamic feature of aircraft requirement using absorbing Markov chain. In conclusion, we suggest a dynamic model to evaluate the number of aircrafts required with key decision variables such as destroying rate, failure rate and repair rate.

• Journal of Korea Water Resources Association
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• v.33 no.1
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• pp.99-110
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• 2000

In this study we proposed a simple method for generating multi-site daily rainfall based on the 1-order Markov chain and considering the spatial correlation. The occurrence of rainfall is simulated by a simple 1st-order Markov chain and its intensity to be chosen randomly from the observed data. The spatial correlation between sites could be conserved as the rainfall intensity at each site is to be chosen consistently with the target site in time through generation. It is found that the generated daily rainfall data reproduce genera] characteristics of the observed data such as average, standard deviation, average number of wet and dry days, but the clustering level in time is somewhat loosened. Thus, the lag-I correlation coefficient of the generated data gave smaller value than the observed, also the average lengths of wet run and dry run and the wet-to-wet and dry-to-dry probabilities were a bit less than the observed. This drawback seems to be overcome somewhat by choosing a proper site representing overall basin characteristics or by use of more detailed states of rainfall occurrence.

• Honam Mathematical Journal
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• v.23 no.1
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• pp.71-90
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• 2001

In this paper, we introduce the MarKov chain and hyperplane arrangement. we prove some properties determined by a hyperplane arrangement and give an example as an application of them.

• Genomics & Informatics
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• v.16 no.4
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• pp.27.1-27.6
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• 2018

The non-coding DNA in eukaryotic genomes encodes a language that programs chromatin accessibility, transcription factor binding, and various other activities. The objective of this study was to determine the effect of the primary DNA sequence on the epigenomic landscape across a 200-base pair of genomic units by integrating 127 publicly available ChromHMM BED files from the Roadmap Genomics project. Nucleotide frequency profiles of 127 chromatin annotations stratified by chromatin variability were analyzed and integrative hidden Markov models were built to detect Markov properties of chromatin regions. Our aim was to identify the relationship between DNA sequence units and their chromatin variability based on integrated ChromHMM datasets of different cell and tissue types.

• KIISE Transactions on Computing Practices
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• v.21 no.1
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• pp.94-99
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• 2015

With the recent machine learning paradigm of using nonparametric Bayesian statistics and statistical inference based on random sampling, the Dirichlet distribution finds many uses in a variety of graphical models. It is a multivariate generalization of the gamma distribution and is defined on a continuous (K-1)-simplex. This paper presents a sampling method for a Dirichlet distribution for the problem of dividing an integer X into a sequence of K integers which sum to X. The target samples in our problem are all positive integer vectors when multiplied by a given X. They must be sampled from the correspondingly gridded simplex. In this paper we develop a Markov Chain Monte Carlo (MCMC) proposal distribution for the neighborhood grid points on the simplex and then present the complete algorithm based on the Metropolis-Hastings algorithm. The proposed algorithm can be used for the Markov model, HMM, and Semi-Markov model for accurate state-duration modeling. It can also be used for the Gamma-Dirichlet HMM to model q the global-local duration distributions.

• The Korean Journal of Applied Statistics
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• v.33 no.1
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• pp.47-59
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• 2020

In this paper, we present the longitudinal Markov binary regression model with t-link function when its transition order is known or unknown. It is assumed that logit or probit models are considered in binary regression models. Here, t-link function can be used for more flexibility instead of the probit model since the t distribution approaches to normal distribution as the degree of freedom goes to infinity. A Markov regression model is considered because of the longitudinal data of each individual data set. We propose Bayesian method to determine the transition order of Markov regression model. In particular, we use the deviance information criterion (DIC) (Spiegelhalter et al., 2002) of possible models in order to determine the transition order of the Markov binary regression model if the transition order is known; however, we compute and compare their posterior probabilities if unknown. In order to overcome the complicated Bayesian computation, our proposed model is reconstructed by the ideas of Albert and Chib (1993), Kuo and Mallick (1998), and Erkanli et al. (2001). Our proposed method is applied to the simulated data and real data examined by Sommer et al. (1984). Markov chain Monte Carlo methods to determine the optimal model are used assuming that the transition order of the Markov regression model are known or unknown. Gelman and Rubin's method (1992) is also employed to check the convergence of the Metropolis Hastings algorithm.

• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.541-550
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• 2003

We consider the generalized autoregressive model with conditional heteroscedasticity process(GARCH). It is proved that if (equation omitted) β/sub i/ < 1, then there exists a unique invariant initial distribution for the Markov process emdedding the given GARCH process. Geometric ergodicity, functional central limit theorems, and a law of large numbers are also studied.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.455-464
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• 2005

In this paper, we analyze a queueing system with overload control by arrival rates. This paper is motivated by overload control to prevent congestion in telecommunication networks. The arrivals occur dependent upon queue length. In other words, if the queue length increases, the arrivals may be reduced. By considering the burstiness of traffics in telecommunication networks, we assume the arrival to be a Markov-modulated Poisson process. The analysis by the embedded Markov chain method gives to us the performance measures such as loss and delay. The effect of performance measures on system parameters also is given throughout the numerical examples.

• The Korean Journal of Applied Statistics
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• v.18 no.1
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• pp.1-13
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• 2005

Latent Class model has been considered recently by many researchers and practitioners as a tool for identifying heterogeneous segments or groups in a population, and grouping objects into the segments. In this paper we consider data on prostate cancer patients from Korean National Cancer Institute and propose a method for grouping prostate cancer patients by using latent class Poisson model. A Bayesian approach equipped with a Markov chain Monte Carlo method is used to overcome the limit of classical likelihood approaches. Advantages of the proposed Bayesian method are easy estimation of parameters with their standard errors, segmentation of objects into groups, and provision of uncertainty measures for the segmentation. In addition, we provide a method to determine an appropriate number of segments for the given data so that the method automatically chooses the number of segments and partitions objects into heterogeneous segments.