What step method should be we using?

[bas-rustenburg]

Copy-paste from #53

Here is something interesting.

I took a look at the different step methods for MCMC. Here is the host concentration, estimated at 1.0157 mM in this particular experiment (I just picked a host-guest titration at random from one of our previous sets of experiments).

Settings:
Using the TwoComponentBindingModel about 320000 iterations (I stopped it at around 16% of 2000000) 10000 burn in iterations and a thinning period of 25. Not sure how good those settings are but there is quite a striking difference.

Using the RescalingStep:

Note that the value on the y-axis is offset by 1.0124
Using a default pymc Metropolis step:

[bas-rustenburg]

Rescaling after about 975000 steps using same settings. Full series of plots

[bas-rustenburg]

Here is the Metropolis data after 1000000:

[bas-rustenburg]

So, an old version of the twocomponentmodel was using it correctly. I think a little too much copy paste action from merging several versions of ITC.py and models.py of yore dropped the metropolis step. Opening a separate PR to fix after the current.

[bas-rustenburg]

CompetitiveBindingModel in it's current form uses both.

[bas-rustenburg]

Copy-paste from #55
Here is the data, fixing the bug so we're using both Metropolis and RescalingStep at once.

1,000,000 steps, 10000 burn-in, thinning period of 25:

[bas-rustenburg]

Comparison, for convenience:
Just Metropolis:

Both Metropolis and RescalingStep:

[jchodera]

Looks like it isn't worth the added complexity right now. Ditch RescalingStep?

[bas-rustenburg]

Sure, will switch back to regular Metropolis. Leaving the (fixed) implementation if we decide tweaking something, so will merge once I set things back to using just Metropolis.