MultiNest

[ben18785]

Created MultiNest sampler and simplified ellipsoidal nested sampling by creating an Ellipsoid class shared by both samplers. Things done:

• Created Ellipsoid class used by both methods
• Added MultiNest which uses a EllipsoidTree class to form a binary tree of ellipsoid leaves which cover the sampling domain
• Corrected some parts of ellipsoidal sampling which meant that ellipsoidal updating wasn't being triggered
• Changed name of sampler -> controller in rejection sampling notebook to avoid ambiguity
• Made a notebook that plots lots of pretty pictures of the ellipsoids produced within MultiNest and shows how the approach works really quite well for the tricky Goodwin Oscillator model

[codecov]

Codecov Report

Merging #1319 (9d949dc) into master (9052e5d) will not change coverage.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##            master     #1319    +/-   ##
==========================================
  Coverage   100.00%   100.00%            
==========================================
  Files           87        88     +1     
  Lines         8933      9190   +257     
==========================================
+ Hits          8933      9190   +257     

Impacted Files	Coverage Δ
pints/_log_priors.py	100.00% <ø> (ø)
pints/_nested/_rejection.py	100.00% <ø> (ø)
pints/__init__.py	100.00% <100.00%> (ø)
pints/_nested/__init__.py	100.00% <100.00%> (ø)
pints/_nested/_ellipsoid.py	100.00% <100.00%> (ø)
pints/_nested/_multinest.py	100.00% <100.00%> (ø)
pints/_mcmc/_mala.py	100.00% <0.00%> (ø)
pints/_mcmc/_nuts.py	100.00% <0.00%> (ø)
pints/_mcmc/_dream.py	100.00% <0.00%> (ø)
pints/_mcmc/__init__.py	100.00% <0.00%> (ø)
... and 12 more

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[MichaelClerx]

Hi Ben!
Some minor comments on the first few files. Will look at the rest at some later point in time :-)

[MichaelClerx]

This is very confusing. You sample from an annulus distribution, and then want to convert it to be within a certain range.
So why not set the parameters for the Annulus so that they end up in that range? Or if they are fixed just scale everything e.g. draws = (draws - lower) / (upper - lower) ?
I don't understand where the gaussian distribution comes in

[ben18785]

Thanks. Yep, I think I just need to explain this better to be honest. The Gaussian distribution comes in as a prior but I hadn't explained this before.

[MichaelClerx]

If these are useful for the user, we should make them public.
Users should never import anything from a hidden _module.

(Also, if you were going to do it, the first line should just be from pints._nested import .... The __init__ file is what determines what lives inside the pints._nested namespace)

[MichaelClerx]

Having said all that, I'm not sure where these should live :D

• pints.EllipsoidTree seems to general?
• pints.MultiNestSampler.EllipsoidTree is possible, but maybe not nice from a code organisation point of view?
• Some new module pints.multinest where these two can live?

[ben18785]

Yeah, I wasn't sure this. The notebook using them for pedagogical purposes (although as your comment above suggests, these bits need to be improved), but, for running MultiNest, they're not necessary. That's why I kept them non-public... I'm happy for them to be public but I just wasn't sure about their utility for a user?

[MichaelClerx]

Wait, the multinest class doesn't use them?

[ben18785]

MultiNest uses them but a user wouldn't need ever to call EllipsoidTree or Ellipsoid (or any of their methods) themselves.

[MichaelClerx]

I dunno. If I was using multinest I think Gary would make me visualise the ellipses to check what it was doing :D

[ben18785]

Hmm, re: location, I'm not sure either. Ellipsoid is required by ellipsoidal nested sampling and multinest; ellipsoidtree is only required by multinest...

[MichaelClerx]

We could change from pints._nested to pints.nested, but only import the samplers?
So then you'd do

import pints
pints.MultiNest

but

import pints.nested
e = pints.nested.Ellipsoid

?

[MichaelClerx]

You'd still be able to do pints.nested.MultiNest, so that would be slightly messy

[MichaelClerx]

From the annulus example, I was expecting the ellipses to encompass the data, but below that doesn't seem to be the case. I guess they're just some characteristic shape of a distribution, e.g. its std dev?

Warrants some comment in the notebook I think

[MichaelClerx]

In the other controllers we handle this in a more general way, by letting each sampler/optimiser define a method _log_init (that does nothing by default) which can update the logging

https://github.com/pints-team/pints/blob/master/pints/_mcmc/__init__.py#L623-L624

and _log_write:

https://github.com/pints-team/pints/blob/master/pints/_mcmc/__init__.py#L820-L821