your posterior dist is wrong, i think it should be 1.44 instead of 0.42
Given (mu,tau)~normal-gamma(2.7,1.08,4,0.2916)
I have worked out the posterior distribution to be
(mu,tau)~normal-gamma(2.47,28.08,17.5,0.42)
From this i have also worked out the means and standard deviations.
I am asked to determine the marginal prior and posterior densities for sigma(which is 1/(square root tau)) and I have to use the theory
f(y)=f(g^-1(y)) d/dy (g^-1(y))
I'm not quite sure how to start.
Do I start with the marginal prior density for the marginal tau~(17.5,0.42)?
Many Thanks