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

계층적 베이지안 혼합 효과 모델을 사용한 비동차 마코프 체인의 분석

  • Received : 2013.12.21
  • Accepted : 2014.02.19
  • Published : 2014.04.30


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.


  1. Chat eld, C. (1973). Statistical inference regarding Markov chain models, Applied Statistics, 22, 7-20.
  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.
  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.
  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.