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I have a model involving two scalar parameters $\theta_1$ and $\theta_2$ and derive 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 compute 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 ?

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 ?

I have a model involving two scalar parameters $\theta_1$ and $\theta_2$ and derive 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 compute 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 ?

I have a model involving two scalar parameters $\theta_1$ and $\theta_2$ and derive 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 compute 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 ?

I have a model involving two scalar parameters $\theta_1$ and $\theta_2$ and derive 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 compute the independent reference prior for $\theta_1$ and $\theta_2$ using the Theorem 2.1 (page 17) 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 ?

I have a model involving two scalar parameters $\theta_1$ and $\theta_2$ and derive 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 compute 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 ?