Empirical Bayes analysis of log-linear models for a generalized finite stationary Markov chain. (English) Zbl 1079.62083
Summary: This article presents an empirical Bayes method for estimation of the transition probabilities of a generalized finite stationary Markov chain whose \(i\)th state is a multi-way contingency table. We use a log-linear model to describe the relationship between the factors in each state. The prior knowledge about the main effects and interactions will be described by a conjugate prior. Following the Bayesian paradigm, Bayes and empirical Bayes estimators relative to various loss functions are obtained. These procedures are illustrated by a real example. Finally, asymptotic normality of the empirical Bayes estimators are established.
MSC:
62M05 | Markov processes: estimation; hidden Markov models |
62C12 | Empirical decision procedures; empirical Bayes procedures |
62H17 | Contingency tables |
62F15 | Bayesian inference |
62E20 | Asymptotic distribution theory in statistics |