Perfect nested sampling functionality

[williamjameshandley]

Description

A set of scripts for generating perfect nested sampling runs which will prove useful in developing techniques such as importance sampling #132.

Changes:

1. Implemented a spherical gaussian as found in John Skilling's original paper
2. Implemented a correlated gaussian, which can be used to simulate cosmological likelihoods
3. Moved the wedding cake class into a function in the same framework as the two above

Checklist:

• I have performed a self-review of my own code
• My code is PEP8 compliant (flake8 anesthetic tests)
• My code contains compliant docstrings (pydocstyle --convention=numpy anesthetic)
• New and existing unit tests pass locally with my changes (python -m pytest)
• I have added tests that prove my fix is effective or that my feature works

[codecov]

Codecov Report

Merging #205 (62d2c17) into master (ba7d4b3) will not change coverage.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##            master      #205    +/-   ##
==========================================
  Coverage   100.00%   100.00%            
==========================================
  Files           26        29     +3     
  Lines         2303      2422   +119     
==========================================
+ Hits          2303      2422   +119     

Impacted Files	Coverage Δ
anesthetic/examples/_matplotlib_agg.py	100.00% <100.00%> (ø)
anesthetic/examples/perfect_ns.py	100.00% <100.00%> (ø)
anesthetic/examples/utils.py	100.00% <100.00%> (ø)
anesthetic/samples.py	100.00% <100.00%> (ø)

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[lukashergt]

This could indeed be useful. Did you intend to add more to this or is this ready for review?

See comments inline.

[williamjameshandley]

I have added a planck gaussian example (anesthetic.examples.planck_gaussian) which produces a gaussian likelihood in 6 cosmological parameters with the correct labels, mean, covariance and normalisation.

One subtlety is that this would not give the same evidence as a full planck run, but we could choose this normalisation a-la-nuisance marginalised likelihoods.

In addition I corrected a bug which testing this threw up (a factor of 2 in the d_G) and improved the efficiency of generating these perfect nested sampling runs (namely updating the bounds on the uniform step, and fixing a bug where previously the bounds were assumed to be 0 and 1 for the elliptical step). These proved essential in making this efficient enough to work with 6 parameters.

It is too inefficient with all nuisance parameters sadly.

[williamjameshandley]

This will also be useful for removing demo.py in #246.

[lukashergt]

See comments inline.

[lukashergt]

Great! Thanks @williamjameshandley, please squash and merge.