2.7 Normal variance
2.7.1 A suitable prior for the normal variance
Suppose that we have an n-sample 
from 
where the variance 
is unknown but the mean μ is known. Then clearly
On writing
(remember that μ is known; we shall use a slightly different notation when it is not), we see that
In principle, we might have any form of prior distribution for the variance . However, if we are to be able to deal easily with the posterior distribution (and, e.g. to be able to find HDRs easily from tables), it helps if the posterior distribution is of a ‘nice’ form. This will certainly happen if the prior is of a similar form to the likelihood, namely,
where κ and S0 are suitable constants. For reasons which ...
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