Resumen
The problem of selecting the best treatment is studied under generalized linear models. For certain balanced designs, it is shown that simple rules are Bayes with respect to any non-informative prior on the treatment effects under any monotone invariant loss. When the nuisance parameters such as block effects are assumed to follow a uniform (improper) prior or a normal prior, Bayes rules are obtained for the normal linear model under more suitable balanced designs, keeping the generality of the loss and the generality of the non-informativeness on the prior of the treatment effects. These results are extended to certain types of informative priors on the treatment effects. When the designs are unbalanced, algorithms based on the Gibbs sampler and the Laplace method are provided to compute the Bayes rules.

Resumen
Let X¯i~N(?i,t2/n), i=1,…,k, be independent sample means, based on a common sample size n from k normal populations with the same known variance t2>0. To select a small non-empty subset that contains with a guaranteed probability P* the best population, i.e. the population associated with ?[k]=max{?1,…,?k}, Gupta [1956. On a decision rule for a problem in ranking means. Ph.D. Thesis, Mimeo, Series No. 150, Institute of Statistics, University of North Carolina, Chapel Hill; 1965. On some multiple decision (selection and ranking) rules. Technometrics 7, 225–245.] proposed and studied a subset selection rule that has become a classic and bears his name. Since then, its performance has been studied and compared with the performance of other subset selection rules by many authors. Gupta and Miescke [2002. On the performance of subset selection rules under normality. J. Statist. Plann. Inference 103, 101–115.] derived generalized Bayes rules under two loss functions and possibly unequal sample mean variances t2/ni, i=1,…,k, but risk comparisons between these generalized Bayes rules and Gupta's classical rule appeared to be infeasible, both theoretically and numerically. With the advent of faster computers, risk comparisons via computer simulations have become feasible. Numerical results of this type for equal sample mean variances are presented in this paper.