Bayesian Statistics: An Introduction, 4th Edition

5.2 Variances unknown but equal

5.2.1 Solution using reference priors

We shall now consider the case where we are interested in and we have independent vectors and such that

so that the two samples have a common variance .

We can proceed much as we did in Section 2.12 on ‘Normal mean and variance both unknown’. Begin by defining

For the moment, take independent priors uniform in λ, μ and , that is,

With this prior, the posterior is

where

It follows that, for given , the parameters λ and