A question of mode_check plot

[Econbee]

Dear all,

I recently encountered a problem when finding the posterior mode. I hope anyone who experienced similar situations could give me some hints or suggestions. The plot has been attached.

Usually, the mode_check plot after finding the mode looks like a smooth concave curve as the middle one in the attached plot. But I also got some cases like the left one and the right one, in which the curve is not a concave one. The highest point is the intersection of two convex curves. I did a very comprehensive search for the mode and always got this result. I am wondering if this situation is normal?

Thanks in advance!

[jpfeifer]

I cannot say much about this, but it looks your prior is relatively wide and the posterior around +- 10% of the mode value seems to concave. Posteriors can be really irregular.

More generally, I am not aware of any argument that a cut through the posterior should be concave for the whole range. It should be concave in an open neighbourhood of the mode, but this seems to be the case.

[Econbee]

Thanks for your prompt reply, jpfeifer!