Consider the linear regression model
$${\bf y} = {\bf X}\beta + {\bf e},$$
where ${\bf y}$ is an $n\times 1$ vector, $\beta$ is a $p\times 1$ vector, ${\bf e}$ is an $n\times 1$ vector. Assume also that $e_j\stackrel{ind.}{\sim} N(0,\sigma)$.
What is the Jeffreys prior of the parameters $(\beta,\sigma)$? I am basically looking for a reference where I can find this.
I have found a reference.
The Jeffreys prior in the normal linear regression model is:
$$\pi(\beta,\sigma^2)\propto \dfrac{1}{(\sigma^2)^\frac{p+2}{4}},$$
or more commonly in the $\sigma$ parameterization:
$$\pi(\beta,\sigma)\propto \dfrac{1}{\sigma^\frac{p+2}{2}}.$$
The reference is: http://www.jstor.org/stable/2290514 (see text just after Eq. 2.9 -- a bit hard to read!)
