# Is Independent jeffreys prior different from independent reference prior?

I have a model involving two scalar parameters $\theta_1$ and $\theta_2$ and derived the Jeffreys prior for $\theta_1$ and $\theta_2$ independently (so for, e.g. $\pi(\theta_1)$, setting in the normalisation constant eveything that concern $\theta_2$, which in my case is possible). Then I computed the independent reference prior for $\theta_1$ and $\theta_2$ using the Theorem 2.1 (page 18) of this dissertation.

I found that these two are different.

1. Is this possible ?
2. If it is the case, is there any intuitive explanations for that ?
• In 1. are you asking if it's possible to have a reference prior that's not a Jeffreys' prior? – Glen_b Feb 6 '16 at 5:57
• @glen_b. No. I am asking if the independent reference prior for $n$ scalar parameters can be different from taking the product of the $n$ Jeffreys prior for each parameter independently (assuming it is possible). – peuhp Feb 6 '16 at 15:48