Estimation bayesienne des effets dans le modele a effets aleatoires de classification double avec interaction
Bernard Clement · Canadian Journal of Statistics · 1975
Abstract The problem of estimating the effects in a balanced two‐way classification with interaction \documentclass{article}\pagestyle{empty}\begin{document}$i = 1, \ldots ,I;j = 1, \ldots ,J;k = 1, \ldots ,K$\end{document} using a random effect model is considered from a Bayesian view point. Posterior distributions ofri,cjandtijare obtained under the assumptions thatri,cj,tijandeijkare all independently drawn from normal distributions with zero meansand variances\documentclass{article}\pagestyle{empty}\begin{document}$\sigma _r^2 ,\sigma _c^2 ,\sigma _t^2 ,\sigma _e^2$\end{document} respectively. A non informative reference prior is adopted for\documentclass{article}\pagestyle{empty}\begin{document}$\mu ,\sigma _r^2 ,\sigma _c^2 ,\sigma _t^2 ,\sigma _e^2$\end{document} . Various features of thisposterior distribution are obtained. The same features of the psoterior distribution for a fixed effect model are also obtained. A numerical example is given.