PyMC3 for physics

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Hi team,

After a brief chat with @fonnesbeck in Southampton, UK a few months back, I thought I would try using the pm.Potential function to help teach MCMC in physics and it seems to work excellently.

I’d be keen to write up a notebook for the documentation if you think it would fit?

Here’s a notebook I produced for our group link. It would need adapting a little but I think an example of the Heisenberg model would be a nice example of how pm.Potential can be used.

I think the important concepts for those looking to use PyMC3 for physics problems would be:

  • Showing how energy and the probability distribution link
  • Explaining the necessity of the prior distributions
  • Plotting the energy and probability surfaces

Any other suggestions?

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This looks awesome! Yes definitely PR a notebook.
My only nitpick: you should rewrite the tot function using theano ops for the sampling in PyMC3.

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Cool!
One problem that could come up here is that the sampler might get stuck in one of the local minima. So I would add a traceplot and also run several chains and check the rhat (pm.gelman_rubin). Our current hamiltonian methods don’t deal with multimodal posteriors particularly well. SMC might help with that, but I don’t know much about it.
Also, with nuts you don’t usually need that many samples (that is, as long as the sampler doesn’t get stuck around one mode for long time)

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Very nice example of using PyMC3 (and pm.Potential) to simulate physical systems!

I think one nice extension to your example will be to include a “kT- term” and suggest the student/user to test values like 0.1, 1 and 10 to explore the role of temperature in the system.

Regarding @aseyboldt comment I want to add that I am using PyMC3 with the SMC sampler to simulate (small) biomolecules with very good results so far :slight_smile: Maybe the energy barrier in your example is relatively low, but for the systems I am using SMC is crucial to avoid getting trapped in local minima.

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All, thanks for suggestions so far (keep them coming!) - I’ll get to work on these.

I haven’t used the sequential MC step in PyMC3 and I couldn’t find any documentation other than the docstring. Is there an example of smc in recent docs build?

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This is awesome, thanks for writing it up!

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Take a look at this notebook

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