Make sure MultimodalNormalLogPDF throws an error when supplying non-posdefinite cov matrix

[ben18785]

The populationMCMC notebook has this, I think.

[MichaelClerx]

If it does that'll be from the underlying scipy / numpy code then (so not something we need to test)

[ben18785]

I don't understand why the below returns a non-zero number:

dist = scipy.stats.multivariate_normal(mean=[16, 12], cov=[[0.8, 0.2], [0.1, 1.4]])
dist.pdf([3, 4])

here cov is not symmetric, so does not satisfy, "The covariance matrix cov must be a (symmetric) positive semi-definite matrix" in the scipy docs...

This looks like a bug in scipy to me! So, we need to test.

[ben18785]

Wrote a bug issue on Scipy: https://github.com/scipy/scipy/issues/13541

[MichaelClerx]

I'm happy for us to stick in a test that the matrix must be symmetric, although we'll run into the precision issues mentioned by the scipy devs.

[ben18785]

It's fine for us not to test it in that case (I do think the scipy reasoning is a bit weak though: if you're afraid of numerical round off, fine, but most other libraries manage to find a sensible middle ground). Although we need to make sure that we use the method properly, so need to fix the populationMC notebook (and more generally check wherever MultiModalLogPDF is called). I'll create a separate ticket for this though and close this one.

On Wed, Feb 10, 2021 at 8:33 AM Michael Clerx [email protected] wrote:

I'm happy for us to stick in a test that the matrix must be symmetric, although we'll run into the precision issues mentioned by the scipy devs.

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[ben18785]

Actually, I'm now less sure: we do have such a test in the GaussianLogPDF, so I'm just going to grab this from there.