Weekly plans and update for week 8 and 9

Hi all, we hope you are doing well. Here comes the standard weekly update with our plans for this and next week.
Last week we attempted at a conclusion on gradient methods and for project 1, the simplest plain gradient descent does a pretty decent job. 
What we have now is
1) a VMC program with brute force and importance sampling
2) hopefully added a gradient descent optimization in order to get the best variational parameter(s).

Now we need to think more carefully about statistical errors and we are going to encounter two much used techniques, the so-called bootstrap technique and the blocking method. 
Hopefully these methods (to be discussed this week and next week) allow us to get a better estimate of the standard deviation and thus our statistical error. 
The learning material is at for example http://compphysics.github.io/ComputationalPhysics2/doc/pub/week8/html/week8-reveal.html or as a jupyter-notebook at http://compphysics.github.io/ComputationalPhysics2/doc/pub/week8/ipynb/week8.ipynb.

We will take again a top-down view first, with an emphasis on what we need to code.
Top down approach first, what we need to code, thereafter we jump into more details on
Resampling Techniques and statistics: Bootstrap and Blocking
The following overview video on the Bootstrap method may be useful https://www.youtube.com/watch?v=O_Fj4q8lgmc&ab_channel=MarinStatsLectures-RProgramming%26Statistics
and similarly the article based on 
Marius Johnson's Master thesis on the Blocking Method, see https://www.duo.uio.no/bitstream/handle/10852/68360/PhysRevE.98.043304.pdf?sequence=2&isAllowed=y

Best wishes to you all,
Morten and ?yvind