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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.

Macro
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Drake
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  • If you want your account deleted just flag the question and leave a comment to the moderator to delete your account.... – Macro Aug 29 '13 at 16:23

1 Answers1

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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!)

Community
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Drake
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  • Most people drop the $(p-2)/2$ term and simply use $$\pi(\beta,\sigma^2)\propto\frac{1}{\sigma^2}$$ –  Aug 29 '13 at 21:51