[MED]: PDE Example Refactor

[mathematicalmichael]

Feature Request

• should be able to specify a distribution independent of a set of samples used for loading
• three datasets should be packaged in 2D: uniform, normal with 95% of samples in (0,4), normal with 99% of samples in (0,4)
• in 1D, same idea.
• in 5D, just uniform
• 1000 samples for each, 100 500 sensors maximum
• stop inferring distribution from filename
• get rid of prefix handling
• be able to create MUD-1D (not just MUD-2D-alt).

Must do:

• default to log likelihoods in mud, don't compute the evidence for the posterior. It causes divide by zero errors.

Nice to haves:

• decouple runner from pde example, make it entirely independent
• pde 1D probably can be separated out since it has a different set of figures
• can we attach the geometry study to the output as well?
• check out contents of results.pkl and decide if it's worth keeping
• refactor the experiment-handling methods to be more transparent in what they are doing. Use dictionaries as configs?

[mathematicalmichael]

Other bugfixes:

• matplotlib fontsize in comparison figures
• rename files to have descriptive names inv -> monomial
• either make a submodule for the linear examples, or separate the contour one out.
• maybe linear.dimension / linear.rank / linear.contours
• nonlinear.pde / nonlinear.ode / nonlinear.monomial
• rand.py should be renamed somehow. random_maps or maybe linear.models is more apt?

[mathematicalmichael]

@eecsu usage examples:

mud_run_pde -d n --loc 0 --scale 1 -m 20 100 500  # unassuming prior
mud_run_pde -d n --loc -2 --scale 0.2 -m 20 100 500  # very nice comparison
mud_run_pde -d n --loc -2 --scale 0.1 -m 20 100 500  # too restrictive

I made extensive use of kwargs to support arbitrary distributions (so, this should work beyond just scipy in theory as long as methods .pdf exist).

if loc/scale not provided as kwargs, then we default to -2, 0.2 in Normal, -4, 4 in Uniform.

code not refactored yet, but the feature is working, and results can be put in front of Troy for review. Warrants a release candidate.

prefix handling is gone, prefix=results hard-coded into make_reproducible_without_fenics, shell scripts not updated.

still infer distribution from file name in order to pass sample_dist as an argument (if u (uniform), then use weighted KDE always... since if the prior/initial is uniform, it's fine, and if normal, beta, etc, then it's using the right tranformation with the weights set as the initial pdf evaluations).

[mathematicalmichael]

also made some headway on moving functions around / modules. tests passing, see #33