Keep in mind that other parameters were varied also, which probably explains some of the overlap seen in the picture.
To find out what this dependence is, we do some tests. Even for a simple problem (one correlator, three energy levels) there are six free parameters, so it's not feasible to just try every starting guess. Instead, I try random guesses, based on what would be tried with reasonable prior widths. The results are then sorted by the final fit result (which will go to one of two (or possibly three) final values, and plotted to look for trends.
The following plot looks at 1000 fits to the b1 local-local correlator for the .01 dataset.
Blue points gave a ground state fit of 2.007952, while red points gave a ground state fit of
1.799898, which we believe to be a spurious state.
Keep in mind that other parameters were varied also, which probably explains some of the
overlap seen in the picture.
I've been testing with the 1S smearing, and with the local+1S+2S smearing, but those results are not yet available. (They're a little more confusing to work with.) I'll try to add them here within the next 24 hours.