• 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.

• Journal of the Korean Data and Information Science Society
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• 제27권5호
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• pp.1241-1251
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• 2016

일정한 시간 간격으로 임의의 점프크기가 계속 누적되는 이산시간 확률보행을 고려한다. 각 시점에서의 점프크기가 이전 시점의 점프크기에 종속되어 결정되는 상관 확률보행과 각 시점에서의 점프크기가 이전 시점의 점프크기와 무관하게 독립적으로 결정되는 무상관 확률보행의 점근적 평균을 각각 계산한다. 그리고 상관 확률보행과 무상관 확률보행을 임의적으로 혼합하여 결합하거나 또는 일정한 패턴에 따라 주기적으로 반복하여 결합하는 혼합 확률보행의 점근적 평균 식을 유도한다. 각 확률보행의 점근적 평균은 0으로 공정한 게임을 나타내지만 두 확률보행을 결합한 혼합 확률보행의 점근적 평균은 음수가 되어 지는 게임이 되거나 또는 양수가 되어 이기는 게임이 되는 파론도 역설 현상이 나타남을 확인하고 해당되는 각 모수의 범위를 찾는다.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제9권7호
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• pp.2568-2584
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• 2015

Spectral clustering has become one of the most popular clustering approaches in recent years. Similarity graph constructed on the data is one of the key factors that influence the performance of spectral clustering. However, the similarity graphs constructed by existing methods usually contain some unreliable edges. To construct reliable similarity graph for spectral clustering, an efficient method based on Markov random walk (MRW) is proposed in this paper. In the proposed method, theMRW model is defined on the raw k-NN graph and the neighbors of each sample are determined by the probability of the MRW. Since the high order transition probabilities carry complex relationships among data, the neighbors in the graph determined by our proposed method are more reliable than those of the existing methods. Experiments are performed on the synthetic and real-world datasets for performance evaluation and comparison. The results show that the graph obtained by our proposed method reflects the structure of the data better than those of the state-of-the-art methods and can effectively improve the performance of spectral clustering.

• 한국지하수토양환경학회지:지하수토양환경
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• 제20권3호
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• pp.51-64
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• 2015

In the present study, we develop two history matching techniques based on Markov chain Monte Carlo method where radial basis function and Gaussian distribution generated by unconditional geostatistical simulation are employed as the random walk transition kernels. The Bayesian inverse methods for aquifer characterization as the developed models can be effectively applied to the condition even when the targeted information such as hydraulic conductivity is absent and there are transient hydraulic head records due to imposed stress at observation wells. The model which uses unconditional simulation as random walk transition kernel has advantage in that spatial statistics can be directly associated with the predictions. The model using radial basis function network shares the same advantages as the model with unconditional simulation, yet the radial basis function network based the model does not require external geostatistical techniques. Also, by employing radial basis function as transition kernel, multi-scale nested structures can be rigorously addressed. In the validations of the developed models, the overall predictabilities of both models are sound by showing high correlation coefficient between the reference and the predicted. In terms of the model performance, the model with radial basis function network has higher error reduction rate and computational efficiency than with unconditional geostatistical simulation.

• Journal of the Korean Data and Information Science Society
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• 제26권3호
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• pp.755-762
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• 2015

One of the main objectives of the U.S. Census Bureau is the proper estimation of median household income for small areas. These estimates have an important role in the formulation of various governmental decisions and policies. Since direct survey estimates are available annually for each state or county, it is desirable to exploit the longitudinal trend in income observations in the estimation procedure. In this study, we consider Fay-Herriot type small area models which include time-specific random effect to accommodate any unspecified time varying income pattern. Analysis is carried out in a hierarchical Bayesian framework using Markov chain Monte Carlo methodology. We have evaluated our estimates by comparing those with the corresponding census estimates of 1999 using some commonly used comparison measures. It turns out that among three types of time-specific random effects the small area model with a time series random walk component provides estimates which are superior to both direct estimates and the Census Bureau estimates.

• Journal of the Korean Statistical Society
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• 제11권2호
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• pp.118-130
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• 1982

Random walks as specia Markov stochastic processes have received particular attention in recent years. Not only the applicability of the theory already developed but also its extension within the frame work of probability measures on algebraic-topological structures such as semigroups, groups and linear spaces became a new challenge for research work in the field. At the same time new insights into classical problems were obtained which in various cases lead to a more efficient presentation of the subject. Consequently the teaching of random walks at all levels should profit from the recent development.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1991년도 한국자동제어학술회의논문집(국내학술편); KOEX, Seoul; 22-24 Oct. 1991
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• pp.136-141
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• 1991

An Overlapping Decomposed Filter(ODF) accomplishing an initial alignment of an INS is proposed in this paper. The proposed filter improves the observable condition and reduces the filtering computation time. Its good performance has been verified by simulation. Completely observable and controllable conditions of INS error model derived from psi-angle approach are introduced under varying sensor characteristics vary. The east components of gyro and accelerometer have to be the first order markov process and the rest of them are the characteristics of the random walk or first order markov process.

• Management Science and Financial Engineering
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• 제19권2호
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• pp.49-53
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• 2013

A Markov-chain Monte Carlo sampling algorithm samples a new point around the latest sample due to the Markov property, which prevents it from sampling from multi-modal distributions since the corresponding chain often fails to search entire support of the target distribution. In this paper, to overcome this problem, mode switching scheme is applied to the conventional MCMC algorithms. The algorithm separates the reducible Markov chain into several mutually exclusive classes and use mode switching scheme to increase mixing rate. Simulation results are given to illustrate the algorithm with promising results.

• Journal of Information Processing Systems
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• 제7권1호
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• pp.17-28
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• 2011

Despite the fact that the deployment of sensor networks and target tracking could both be managed by taking full advantage of Voronoi diagrams, very little few have been made in this regard. In this paper, we designed an optimized barrier coverage and an energy-efficient clustering algorithm for forming Vonoroi-based Wireless Sensor Networks(WSN) in which we proposed a mobile target tracking scheme (CTT&MAV) that takes full advantage of Voronoi-diagram boundary to improve detectability. Simulations verified that CTT&MAV outperforms random walk, random waypoint, random direction and Gauss-Markov in terms of both the average hop distance that the mobile target moved before being detected and lower sensor death rate. Moreover, we demonstrate that our results are robust as realistic sensing models and also validate our observations through extensive simulations.

• 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.