Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Bayesian Conjugate Analysis for Transition Probabilities of Non-Homogeneous Markov Chain: A Survey

  • Received : 2013.12.17
  • Accepted : 2014.02.12
  • Published : 2014.03.31
Download PDF
⟨ Previous Next ⟩

Abstract

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.

Keywords

References

  1. Anderson, T. W. and Goodman, L. A. (1957). Statistical inference about Markov chains, The Annals of Mathematical Statistics, 28, 89-110. https://doi.org/10.1214/aoms/1177707039
  2. Bernardo, J. M. and Smith, F. M. (1994). Bayesian Theory, John Wiley & Sons, New York.
  3. Billingsley, P. (1961). Statistical methods in Markov chains, The Annals of Mathematical Statistics, 32, 12-40. https://doi.org/10.1214/aoms/1177705136
  4. Duncan, G. and Lin, L. (1972). Inference for Markov chains having stochastic entry and exit, Journal of the American Statistical Association, 67, 761-767. https://doi.org/10.1080/01621459.1972.10481289
  5. 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.
  6. Meshkani, M. R. and Billard, L. (1992). Empirical Bayes estimators for a finite Markov chain, Biometrika, 79, 185-193. https://doi.org/10.1093/biomet/79.1.185
  7. Morris, C. N. (1983). Parametric empirical Bayes inference: Theory and applications, Journal of American Statistical Association, 78, 47-65. https://doi.org/10.1080/01621459.1983.10477920
  8. Nhan, N. (1998). Assessing Change Among Patients in Residential Treatment, Technical Report, Graydon Manor Research Department, Virginia.
  9. Spiegelhalter, D., Thomas, A., Best, N. and Gilks, W. (1996). Bayesian Inference Using Gibbs Sam-pling Manual (version ii), MRC Biostatistics University, Cambridge University.
  10. Spiegelhalter, D., Best, N., Carlin, B. and van der Linde, A. (2002). Bayesian Measures of Model Complexity and Fit (with discussion), Journal of the Royal Statistical Society, Series B, 64, 583-639. https://doi.org/10.1111/1467-9868.00353
  11. Sung, M., Soyer, R. and Nhan, N. (2007). Bayesian analysis of non-homogenous Markov chains:Application to mental health data, Statistics in Medicine, 26, 3000-301 https://doi.org/10.1002/sim.2775