A question of mode_check plot

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!
MyCheckPlot.rar (3.62 KB)

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.

Thanks for your prompt reply, jpfeifer!