ramess101
commented
7 years ago Hi, Rich-
Sorry to take so long to respond. Hope graduation went well! Looking like an icy drive for us to Utah tomorrow.
Ø MBAR _LJ_two_states is a very simple python code that helps demonstrate what I was trying to explain yesterday. Essentially, if I only use configurations from state 0 I get a very poor prediction of internal energy and density for state 1. You were correct in your assumption that the reason why this is happening is because state 1 only has a single configuration that has a non-negligible weight (sample 986). The sigma and epsilon values are different by about 1% and 3%, respectively, for states 0 and 1. I guess I am surprised that this small of a deviation in sigma and epsilon would result in such poor overlap.
Yep, that’s what I’m getting as well. They key statistic to look at here is the distribution of the difference in dimensionless energies, in this case, u_kn[1,:]-u_kn[0,:] has a standard deviation of 5-6 kT, which is a little too big. In particular, there’s one at -67 (which is the one that has the highest weight of 0.66), where the average is about -80, so 13 kT away; the next nearest is at -70, so it’s ~exp(-3) lower in weight – and the rest, even lower.
So, from the distribution of energy differences, this is what one would expect. So the questions is, is that what one would expect from the changes in sigma and epsilon?
Partly it has to do with the number of particles involved. The larger the system, the larger a change of energies will be. So as the system becomes bigger, any change in parameters will result in fluctuations that will be arbitrarily large, and result in poor estimates.
That’s the overall theory. On a practical side, the question is whether one can ask the questions of interest with a system of a small enough size.
Ø MBAR_sampling_LJ_methane is a modified version of the code that you provided me. It requires a few of the additional files that you provided me in lj_bayesian (outlined in the README file). I believe that this file demonstrates that the previous conclusion described for MBAR_LJ_two_states is a general one. In other words, the expectation values for all 91 other states are not accurate when they are obtained using configurations from only state 0. Again, it looks like this is a weighting/overlap issue. (Note that I have changed line 465 so that the data are only imported from state 0 when load_ukln is set to true.)
That’s probably true. In order to span a large range of states, we needed to sample from 91 states. Levi’s 2016 paper showed how could pick new states to span a phase space volume in a relatively straightforward manner. But if you start with just one state, then your radius of prediction is kind of low.
Michael,
I have invited you to collaborate on two github repositories, "MBAR_LJ_two_states" and "MBAR_sampling_LJ_methane".
MBAR _LJ_two_states is a very simple python code that helps demonstrate what I was trying to explain yesterday. Essentially, if I only use configurations from state 0 I get a very poor prediction of internal energy and density for state 1. You were correct in your assumption that the reason why this is happening is because state 1 only has a single configuration that has a non-negligible weight (sample 986). The sigma and epsilon values are different by about 1% and 3%, respectively, for states 0 and 1. I guess I am surprised that this small of a deviation in sigma and epsilon would result in such poor overlap.
MBAR_sampling_LJ_methane is a modified version of the code that you provided me. It requires a few of the additional files that you provided me in lj_bayesian (outlined in the README file). I believe that this file demonstrates that the previous conclusion described for MBAR_LJ_two_states is a general one. In other words, the expectation values for all 91 other states are not accurate when they are obtained using configurations from only state 0. Again, it looks like this is a weighting/overlap issue. (Note that I have changed line 465 so that the data are only imported from state 0 when load_ukln is set to true.)
I guess you already explained why this is the case, my only questions are:
Let me know if the code or plots are unclear.
Thanks
Rich