Bayesian Statistics: An Introduction, 4th Edition

6.5 Comparison of several means – the one way model

6.5.1 Description of the one way layout

Sometimes we want to compare more than two samples. We might, for example, wish to compare the performance of children from a number of schools at a standard test. The usual model for such a situation is as follows. We suppose that is a vector of unknown parameters and that there are independent observations

from I independent populations with, however, a common variance . For simplicity, we shall assume independent reference priors uniform in and , that is

The likelihood is

where

and so the posterior ...