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Bayesian analysis of non‐homogeneous Markov chains: Application to mental health data
Author(s) -
Sung Minje,
Soyer Refik,
Nhan Nguyen
Publication year - 2006
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.2775
Subject(s) - categorical variable , markov chain monte carlo , computer science , markov chain , inference , bayesian probability , variable order bayesian network , covariate , bayesian inference , homogeneity (statistics) , markov model , econometrics , data mining , machine learning , artificial intelligence , mathematics
In this paper we present a formal treatment of non‐homogeneous Markov chains by introducing a hierarchical Bayesian framework. Our work is motivated by the analysis of correlated categorical data which arise in assessment of psychiatric treatment programs. In our development, we introduce a Markovian structure to describe the non‐homogeneity of transition patterns. In doing so, we introduce a logistic regression set‐up for Markov chains and incorporate covariates in our model. We present a Bayesian model using Markov chain Monte Carlo methods and develop inference procedures to address issues encountered in the analyses of data from psychiatric treatment programs. Our model and inference procedures are implemented to some real data from a psychiatric treatment study. Copyright © 2006 John Wiley & Sons, Ltd.