Add methods to compute overlap and effective sample sizes for BAR?

[jchodera]

@mrshirts : What do you think about adding a corresponding computeOverlap() method for BAR? This could help users identify when the BAR uncertainty estimate will be unreliable.

[mrshirts]

I shouldn't be too tough, since the right way is, I think, to just run it through MBAR with 2 states and write a wrapper around it.

[jchodera]

It would also be great to add a method to compute the effective number of samples.

[mrshirts]

Again, would just require calling MBAR as well as BAR and adding that information. THOUGH - actually might be a bit harder, since MBAR wants energies, not energy differences. Maybe would take some more playing around.

[jchodera]

THOUGH - actually might be a bit harder, since MBAR wants energies, not energy differences.

This is not a problem---we did something similar for the MBAR paper with the double optical trap.

We would just form a u_kn matrix where the first N_f values of w_f = u_kn[1,0:N_f] - u_kn[0,0:N_f] and the second N_r values have w_r = u_kn[0,N_f:(N_f+N_r)] - u_kn[1,N_f:(N_f+N_r)]. I think this would be

u_kn = np.zeros([2, N_f + N_r])
u_kn[1,0:N_f] = w_f
u_kn[0,N_f:(N_f+N_r)] = w_r

You can easily check you have it right by computing the free energy difference between the two states 0 and 1 and confirming it reproduces BAR

I may have k and n swapped, but the fact that this is a bit tricky for others to tackle is another reason to wrap the logic in a convenient method within BAR.