When you arrive at "the final result" with correlated and uncorrelated plots, is the y-axis the average CV value or the average free energy/bias? if it's the average CV value, how do you convert that into its corresponding free energy?
The y axis is the average CV value. You cannot convert the average CV into the value of the free energy. You would use a similar technique to calculate block averages on an estimate of the histogram though. You might find the videos on this page useful to help understand those ideas: www.notion.so/Histogram-2d2527795f0140008b318d3bc958ee4c
Very good! So, I will need to do the block averages if I collect the data step by step or between near steps? If I collect the data from equilibration, for example, each 10000 steps, I could calculate the averages without blocking, since I take each sample far enough from previous steps? However, if I still find correlated data even in 10000 steps difference, I need to do the blocking then?
Can you please clarify why the final error is not similar to usual std. deviation (sqrt of variance)? Why there is Nb in the denominator within square root? 16:03
You need to think about the result you are quoting. This quantity is a sample mean that is calculated from N_b samples. The expectation for this quantity is the same as the ensemble average. Importantly, however, the distribution that you are sampling when you calculate this quantity is NOT the canonical distribution. The error therefore cannot be calculated by calculating the fluctuations (i.e. the variance). The distribution that you are sampling from is the distribution for the sample mean that is calculated from N_b identical and independent random variables. If the expectation variable you have sampled is m and the variance is v then the expectation and variance of the sample mean are m and v/N_b. These results are derived in these two videos: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-qfThUCzX4g0.html ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-GDP4VeNfUhg.html I hope this helps.
