Integrate Slice Sampling: Hyperrectangles-based Methods.

[lorcandelaney]

See #772

Includes:

1. Hyperrectangles-based methods for Slice Sampling: Adaptive and Non-Adaptive. Both methods are in pints/pints/_mcmc/_slice_hyperrectangles.py.
2. Tests for Hyperrectangles-based methods.
3. Notebooks for Hyperrectangles-based methods.

[codecov]

Codecov Report

Merging #895 into master will not change coverage.
The diff coverage is 100%.

@@          Coverage Diff          @@
##           master   #895   +/-   ##
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  Coverage     100%   100%           
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  Files          55     56    +1     
  Lines        5673   5772   +99     
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+ Hits         5673   5772   +99

Impacted Files	Coverage Δ
pints/_mcmc/_slice_hyperrectangles.py	100% <100%> (ø)

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[MichaelClerx]

Hey @lorcandelaney ! For these and other PRs, please check how your docstrings render, and if you're using the correct syntax (:math:`1 + x` for maths, ``1 + x`` for code) everywhere!

See CONTRIBUTING.md for instructions on locally building and inspecting the docs

[ben18785]

Great stuff Lorcan -- looking really good! Apart from the inline comments, just one ask from me:

• Can you go through the text in the notebook examples once more? I noticed a few spelling mistakes in there (these are hard to comment on in Github's interface).

[ben18785]

Can we sort this so it's alphabetical please (sorry)?

[ben18785]

Change to, "This example shows how to perform Bayesian inference on multiple toy problems..."

[ben18785]

no capitalisation on slice sampling and adaptive hyperrectangles

[ben18785]

This bit doesn't seem to be parseing for me. Can you check the formulae?

[ben18785]

rejectedvsample -- think a spelling issue

[ben18785]

Where is R_i set?

[ben18785]

Is rejection sampling used for step 4? For example, if a point is drawn that is in the rectangle not in the slice, then it is rejected, right? Can we say this explicitly?

[ben18785]

Is it the gradient of f(x) or of log f(x)?

[ben18785]

Again, is it the gradient of log f(x) of f(x)?

[ben18785]

What happens if adaptation is turned off? Is None returned in grad?

[MichaelClerx]

Please install PINTS, using e.g. pip install -e .[dev,test] (see the README and CONTRIBUTING).
After that these lines import os and os.chdir won't be necessary anymore and can be removed

[MichaelClerx]

Do we really need 2000 iterations for a unimodal Gaussian? Keep in mind these notebooks should run quickly for users, and are tested regularly, so the faster the better!

[MichaelClerx]

Again, based on the trace plots it looks like 2000 iterations is massive overkill

[MichaelClerx]

Comment doesn't match code (and again, do we need 2000?)

[MichaelClerx]

Never say something's obvious! (or trivial etc.)
If readers get it you're wasting space, if they don't you're making them feel bad

[MichaelClerx]

Again please have a look at the number of iterations in all these examples

[MichaelClerx]

See Ben's comments on previous notebook

[MichaelClerx]

This should be :math:`stuff` , same goes for rest of code!

[MichaelClerx]

Please remove these lines, as the debug variable isn't used anywhere.

[MichaelClerx]

Please remove

[MichaelClerx]

Hi @lorcandelaney , have made some initial suggestions to go with @ben18785 's comments.
Overall, it's looking very good!

One question: it seems the two notebooks are very similar, and mostly showcase the same code (just with the adaptive option switched on and off). Would it be better to replace this with a single notebook that shows how the adaptive method is better/worse in selected cases?

[MichaelClerx]

This means if (type(w) == int) or float)
and if float == True...

use np.isscalar(w) instead

[MichaelClerx]

if np.any(w < 0)