Sample Posterior Predictive Behavior

[ColCarroll]

This is a proposal to update sample_posterior_predictive behavior.

Consider:

with pm.Model():
    x = pm.Normal('x')
    y = pm.Normal('y', mu=x, observed=1)
    posterior = pm.sample(draws=500, chains=4)
    posterior_predictive = pm.sample_posterior_predictive(posterior)

print(posterior_predictive['y'].shape)

I propose this should print (2000,).

Current behavior is (500,), and the implementation is roughly:

indices = np.random.randint(0, len(trace), samples)
for idx in indices:
    point = trace[idx]
    ppc_samples = draw_values([var], point=point)
return np.array(ppc_samples)

Good things:

• Supports any number of samples
• They are asymptotically coming from the posterior predictive distribution
• Samples are perhaps less correlated

Bad things:

• Ignores all but the first chain
• Ignores some of the first chain's posterior samples too
• Can not match posterior samples with ppc draws for diagnostics (this came up in arviz)

This would be a reasonably large breaking change! In a perfect world, I would want the return value to always be (4, 500), but if we make it so .reshape(4, 500) matches up with the shape of the full trace. My suggestion is:

• Change the default to what I have described,
• Add a shuffle argument
• If samples is bigger than 2000 and shuffle is False, cycle back over the posterior (in order).

[junpenglao]

Ignores all but the first chain

That's not quite the case - it randomly samples from all 2000 posterior samples and generates 500 posterior predictive samples.

https://github.com/pymc-devs/pymc3/blob/14b3fd01340c269dcc086e5b12e1bc503502c16e/pymc3/sampling.py#L1126-L1131

[ColCarroll]

You're right, thanks - I read line 1131 from there, instead of 1129. I'll update the issue.

[junpenglao]

Cool - also

Add a shuffle argument

is probably not needed.

I am curious about the context of the purpose change: is it for it to easier to work with using arviz? i guess Stan return the posterior predictive samples the same (chains, draws, ...) shape as the MCMC samples.

[twiecki]

So really the proposal is to sample the number of total samples, which makes sense to me.

[ColCarroll]

junpenglao - Yes, the impetus for this is in ArviZ, the dimensions allow you to select by chain and draw, so having that consistent would be nice. I could imagine ppc joint scatter plots being interesting (or maybe not interesting at all?) The scatter plots would require that these dimensions be aligned.

twiecki - This would also stop shuffling the samples (which seems fine to me)

This seems like a positive enough response that I'll make a PR!

[OriolAbril]

@ColCarroll @junpenglao @twiecki I had some trouble trying to understand how posterior predictive sampling worked until I looked at the source code. If it is ok with you I will submit a PR to expand the docs a little and I was also thinking in logging some warning when samples != nchains*ndraws. Or at least when samples<<nchains*ndraws, as whole chains are not taken into account.

I am not really sure about the use of size parameter (and even though ArviZ has no support for it, there are no issues related yet). Can I discourage its use in the docs?

[twiecki]

@OriolAbril That would be much appreciated.