Improve feedback on "Should have \sum_n W_nk = 1" warning

[mrshirts]

The most cited problem is resolving the "Warning: Should have \sum_n W_nk = 1" which occurs when the MBAR solver does not converge, and is virtually always caused by not having sufficient overlap between states (see #320,#292,#323,#317)

I will try to write instructions to help people fix their input to avoid this warning.
One question: should it try to put all the options in the text, or would it be better to have the text of the warning refer to a section of the readthedocs site? I'm leaning towards the latter, since we can include graphs, etc. there.

It's possible there are other bits of information I can extract as well from the state of the system to identify other problems, which I can also try to identify.

[SimonBoothroyd]

should it try to put all the options in the text, or would it be better to have the text of the warning refer to a section of the readthedocs site?

+1 for a one line summary + a link to readthedocs.

[jchodera]

Can we do a bit more computation afterwards before we raise the exception? For example, if we can identify that the data is not self-consistent, this can suggest a units or convergence issue.

[mrshirts]

identify that the data is not self-consistent

We can definitely do some stuff. Some things we could do:

• Make sure that E_ij = E_ij - E_jk
• Make sure there is no numerical overflow.
• Run BAR between neighboring states to see if those converge
• Look at forward and reverse distributions (generate from neighboring states) and look at overlap

What other options are there?