Add MCMC solver to Pastas

[raoulcollenteur]

Short Description

In this PR a MCMC solver based on Emcee is added to Pastas. Here are the most important changes:

• Add new solver: EmceeSolve. I have extensively tested this and I think it is working fine. However, since this is new, I will add a warning message if it is used: "EmceeSolve is still experimental and arguments may change in next version of Pastas".
• Add prior distributions to parameters. All parameter DataFrames throughout Pastas now have a new column "dist", where a distribution for the prior can be provided. This does to affect any of the functionality, but is required for MCMC.
• Add objective functions that can be chosen (e.g., which likelihood function to use). For now two are implemented for Gaussian (autocorrelated) residuals. I think this is a cool feature, because it allows someone to write a new objective functions / likelihood function!
• A notebook is added which gives more information on how to use the new solver and how to apply different settings.

This does not add dependencies, but if one wants to use it emcee and corner should be installed.

Checklist before PR can be merged:

• closes issue [DEVELOPMENT] Add EmceeSolve for MCMC #559
• is documented
• Format code with Black formatting
• type hints for functions and methods
• tests added / passed
• Example Notebook (for new features)
• Remove output for all notebooks with changes

I think the current implementation works well, so curious to hear what you all think about it!

Cheers,
Raoul

[codacy-production]

Coverage summary from Codacy

Merging #572 (9945c38) into dev (cb06df7) - See PR on Codacy

Coverage variation	Diff coverage
❌ -0.21% (target: +0.00%)	77.93%

Coverage variation details

	Coverable lines	Covered lines	Coverage
Common ancestor commit (cb06df7)	4955	3599	72.63%
Head commit (9945c38)	5113 (+158)	3703 (+104)	72.42% (-0.21%)

Coverage variation is the difference between the coverage for the head and common ancestor commits of the pull request branch: <coverage of head commit> - <coverage of common ancestor commit>

Diff coverage details

	Coverable lines	Covered lines	Diff coverage
Pull request (#572)	213	166	77.93%

Diff coverage is the percentage of lines that are covered by tests out of the coverable lines that the pull request added or modified: <covered lines added or modified>/<coverable lines added or modified> * 100%

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[dbrakenhoff]

Nice, this looks cool!

Besides the comments I made in the code a couple of comments here:

• Perhaps it would be interesting to compare the priors and posteriors for one or more parameters in the example notebook?
• Can we help the user a bit more selecting some default emcee parameters, if that is possible?
• Add emcee group to pyproject.toml with optional packages: [emcee, corner, tqdm]?

[raoulcollenteur]

Nice, this looks cool!

Thanks for the review! I made all the your suggested in the notebook and code. I think

Besides the comments I made in the code a couple of comments here:

• Perhaps it would be interesting to compare the priors and posteriors for one or more parameters in the example notebook?

I will note this one down for a future development :)

• Can we help the user a bit more selecting some default emcee parameters, if that is possible?

Not really to be honest, if people want to use this solver they should really read the emcee docs before. I removed some of the defaults in the docstrings, and in the notebook I just want to show how to use them. Then users can figure this out themselves for now. In later stage after we got some more experience with the solver ourselves we may be able to give more guidance..

• Add emcee group to pyproject.toml with optional packages: [emcee, corner, tqdm]?

Yes, Done!

Let me know if all is good and if I may merge :)

Cheers,
Raoul

[dbrakenhoff]

Looks good!