DOI QR코드

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계층적 베이지안 혼합 효과 모델을 사용한 비동차 마코프 체인의 분석

Bayesian Hierarchical Mixed Effects Analysis of Time Non-Homogeneous Markov Chains

  • 투고 : 2013.12.21
  • 심사 : 2014.02.19
  • 발행 : 2014.04.30

초록

본 연구에서는 비동차 마코프 체인에서 개체들의 전이 행태를 분석하기 위한 계층적 베이지안 방법론을 사용하여 혼합 효과 모델을 소개 하였다. 모델의 모수들에 대한 사후분포가 분석적으로 구해질 수 없는 형태를 가지기 때문에 깁스(Gibbs) 샘플링 시뮬레이션 방법을 사용하여 조건부 사후확률로부터 샘플이 추출되었고, 실제 자료분석을 예를 사용하였다.

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.

키워드

참고문헌

  1. Chat eld, C. (1973). Statistical inference regarding Markov chain models, Applied Statistics, 22, 7-20. https://doi.org/10.2307/2346299
  2. Erkanli, A., Soyer, R. and Angold, A. (2001). Bayesian analyses of longitudinal binary data using Markov regression models of unknown order, Statistics in Medicine, 20, 755-770. https://doi.org/10.1002/sim.702
  3. Gelfand, A. E. and Smith, A. F. M. (1990). Sampling-based approaches to calculating marginal densities, Journal of American Statistical Association, 85, 972-985. https://doi.org/10.1080/01621459.1990.10474968
  4. Lee, T. C., Judge, G. G. and Zellner, A. (1970). Estimating the Parameters of the Markov Probability Model from Aggregate Time Series Data, North-Holland and Pub. Co., Amsterdam.
  5. Nhan, N. (1998). Assessing Change Among Patients in Residential Treatment, Technical Report, Graydon Manor Research Department, Virginia.
  6. Spiegelhalter, D., Thomas, A., Best, N. and Gilks, W. (1996). Bayesian Inference Using Gibbs Sampling Manual (version ii), MRC Biostatistics Unit, Cambridge University.
  7. Sung, M., Soyer, R. and Nhan, N. (2007). Bayesian analysis of non-homogenous Markov chains: Application to mental health data, Statistics in Medicine, 26, 3000-3017. https://doi.org/10.1002/sim.2775