5.5 Inferences concerning a variance ratio
5.5.1 Statement of the problem
In this section, we are concerned with the data of the same form as we met in the Behrens–Fisher problem. Thus say, we have independent vectors 
and 
such that
where all of 
are unknown. The difference is that in this case the quantity of interest is the ratio
of the two unknown variances, so that the intention is to discover how much more (or less) variable the one population is than the other. We shall use the same notation as before, and in addition we will find it useful to define
Again, we shall begin by assuming a reference prior
As was shown in Section 2.12 on ‘Normal mean and variance both unknown’, the posterior distributions of and ψ are independent and such that and so that
It turns out that has (Snedecor’s) ...
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