Profiles do not show if dropoff due to bound hitting

[Doresic]

When profiling it is not currently shown whether a dropoff in the likelihood is due to the data constraining the parameter value or whether there really is some structural identifiability but the dropoff happens because the other parameter hits a bound and is not able to progress along the non-identifiability valley.

For instance
If there is a structural non-identifiability that constrains a ratio of two parameters k1 and k2 to be constant, then the profile should be completely flat.
But if, as k1 is increasing, k2 hits its upper bound, the profiling is not able to keep the ratio optimally constant. Thus the likelihood drops off.

This would be fixed by either reporting whether the profiling hits a bound in any other parameter and when plotting the profile using a different marker for these points.

Alternatively, one can look at 2d plots of the profiling to see whether other parameters hit a bound as they progress through the value of the profiling parameter.

[PaulJonasJost]

I think that is a great idea. I am not sure whether 2D plots are sufficient, as it will only be able to capture singular dependencies. D2D has some very nice visualizations for this (see this pdf page 7 specifically for an example). They visualize the profile likelihood and beneath how all other parameters develop in comparison to the profiled parameter. I think a plot like this would be much more advantageous for analysis.

[Doresic]

Nicee, yeah that visualization also looks pretty nice
What I had in mind was this

So you would see all parameter profiles together with the scatter plot of the profiled parameter against all other parameters in the corresponding column.
So it would be able to capture all dependencies, I think.
I'm afraid the visualization from D2D might become very crowded with many parameters, so it would be difficult to keep track of all the parameters, especially if the profiles are very discontinuous.