# When Jeffreys prior “fails”

Context: I am working on a calibration problem involving a 1D function of parameter $\theta$ for which I derived a Jeffreys prior (in fact a 2D but I have an informative prior for one of the parameters).

Observation: Using this prior gives me in practice very bad inference results. Paralelly when using a default choice of the form : $\theta \sim \mathcal{N}(o,1000^2)$ where $o$ is a typical value I get pretty good results.

Question:

What to do in such a situation (expect checking formulas and code) ? what does it means about my model/data ?

I guess this question is quite abstract but any suggestion or remark would help me.

• How do you derive the Jeffreys prior on the other parameter once you have given a prior to the other parameter ? – Stéphane Laurent Mar 30 '14 at 11:59
• @StéphaneLaurent, the Jeffreys prior is computed independently from other parameters. – peuhp Mar 31 '14 at 12:33
• I don't understand exactly what you are doing. A valuable way consists in integrating the likelihood with respect to the first prior and then to take the Jeffreys prior for the marginal (integrated) likelihood. I could explain this in an answer if you precise what you are doing in your question (the model and your method). – Stéphane Laurent Mar 31 '14 at 12:40