Fong, Duncan K. H.; Berger, James O. Ranking, estimation and hypothesis testing in unbalanced two-way additive models: A Bayesian approach. (English) Zbl 0776.62026 Stat. Decis. 11, No. 1, 1-24 (1993). The two-factor additive model with no interactions is considered where the sample sizes are unequal and the errors are normal with known or unknown variance. The Bayesian approach naturally assumes that the main effects are random effects. The objective is to estimate the largest main effects and their standard errors and to obtain the posterior probabilities that each main effect is the largest.It is shown that whatever the number of levels of each factor, at most five-dimensional numerical integration is required to evaluate these probabilities. Reviewer: P.W.Jones (Keele) Cited in 5 Documents MSC: 62F15 Bayesian inference 62J10 Analysis of variance and covariance (ANOVA) 65C99 Probabilistic methods, stochastic differential equations Keywords:unbalanced designs; hierarchical Bayes; exchangeability; Monte Carlo integration; ranking probabilities; ML-estimator; two-factor additive model; random effects; largest main effects; standard errors; posterior probabilities Citations:Zbl 0052.154 PDFBibTeX XMLCite \textit{D. K. H. Fong} and \textit{J. O. Berger}, Stat. Decis. 11, No. 1, 1--24 (1993; Zbl 0776.62026)