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Add error analysis tutorial #4174

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merged 1 commit into from
Aug 2, 2021
Merged

Add error analysis tutorial #4174

merged 1 commit into from
Aug 2, 2021

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biermanncarl
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Description of changes:

  • Adds a tutorial that teaches users the basics of error analysis.

This will solve the tutorial side of issue #3958

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@biermanncarl biermanncarl changed the title Add Error analysis tutorial WIP Add Error analysis tutorial Mar 24, 2021
@KaiSzuttor KaiSzuttor marked this pull request as draft March 24, 2021 13:17
@jonaslandsgesell
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jonaslandsgesell commented Mar 25, 2021 •
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I would propose to generate a correlated time-series via for example the AR-1 process. This is trivial. It will save a lot of time in the generation of the time-series and you can make the discussion independent of MD/MC sampling. I would also refer to the Markov-Chain central limit theorem. This is the straight forward way to introduce the error estimate like it can be found in the paper by Janke.

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Do these tutorials need to be tested? They don't rely on ESPResSo, at all, but only NumPy, Matplotlib and SciPy.

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jngrad commented May 12, 2021

Do these tutorials need to be tested? They don't rely on ESPResSo, at all, but only NumPy, Matplotlib and SciPy.

Yes, all tutorials need to be tested. It's the only way to be sure that the solution cells indeed work. You can add np.random.seed(42) at the beginning of the test to fix the seed and get reproducible random sequences, and check that the final standard error of the mean and autocorrelation time are correct.

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jngrad reviewed May 25, 2021
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First round of comments, more to come this week.

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Plotting the analytical autocorrelation function (see B_n in https://en.m.wikipedia.org/wiki/Autoregressive_model ) in the plot where you show the estimated auto correlation function could be interesting to the reader?

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The proposed changes are in jngrad/espresso@error-analysis-tutorial.

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jonaslandsgesell commented Jul 14, 2021 •
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Did you consider teaching bootstrap and showcasing https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.bootstrap.html#scipy.stats.bootstrap ?

Scipy does not seem to use block bootstrap which is needed for correlated time series data.
Potentially, this python package could be showcased:
https://pypi.org/project/recombinator/

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jngrad commented Jul 30, 2021

Teaching bootstrapping would make this tutorial quite long. We also want to limit the number of python dependencies in ESPResSo.

@jngrad jngrad self-assigned this Jul 30, 2021
@biermanncarl @jonaslandsgesell @jngrad
docs: Add tutorial on error estimation
4856dba 
Teach error analysis of observables using correlated simulation data.

Co-authored-by: Jonas Landsgesell <jonaslandsgesell@users.noreply.github.com>
Co-authored-by: Jean-Noël Grad <jgrad@icp.uni-stuttgart.de>
@jngrad jngrad changed the title WIP Add Error analysis tutorial Add error analysis tutorial Aug 2, 2021
@jngrad jngrad marked this pull request as ready for review August 2, 2021 11:00
@jngrad jngrad added this to the Espresso 4.2 milestone Aug 2, 2021
@jngrad jngrad added the automerge Merge with kodiak label Aug 2, 2021
@kodiakhq kodiakhq bot merged commit 0bf872c into espressomd:python Aug 2, 2021
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