Plans for the week of March 4-8

Dear all, welcome back!  The plan this week is to introduce another important element to our Monte Carlo machinery, namely the inclusion of resampling techniques. These are statistical analysis tools which aim at getting better estimates of various expectation values and their corresponding errors (read standard deviations). We will focus on the Blocking method and the bootstrap method, two popular methods used in the post-analysis of our data. The plan is as follows

Topics.

• Reminder from last week on optimization methods

• Resampling Techniques and statistics: Bootstrap and Blocking

   

   

   

Teaching Material, videos and written material.

• Overview video on the Bootstrap method, see link https://www.youtube.com/watch?v=O_Fj4q8lgmc&ab_channel=MarinStatsLectures-RProgramming%26Statistics

• 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.

Else, the jupyter-notebook for this week is at https://github.com/CompPhysics/ComputationalPhysics2/blob/gh-pages/doc/pub/week8/ipynb/week8.ipynb

See you soon and best wishes.

Daniel, Håkon, and Morten

p.s. For the bootstrap method, detailed proofs can be found in for example https://www.stat.purdue.edu/~dasgupta/bootstrap.pdf