Add a function to generate prior samples

[rlouf]

Here we add a utility function to generate prior samples for any variable present in a model. The function should return samples in a format that is convenient for the users. The format is still TBD, although the standard in the Python PPL world seems to be XArray (for compatibility with ArviZ).

import aesara
import aesara.tensor as at

from aemcmc.sample import sample_prior

srng = at.random.RandomStream(0)
mu_rv = srng.normal(0, 1)
Y_rv = srng.normal(mu_rv, 1.0)

num_samples = at.scalar()
samples, updates = sample_prior(srng, num_samples, Y_rv, mu_rv)
sample_fn = aesara.function([num_samples], samples, updates=updates)
sample_fn(10)

Note: it is not necessary to pass the updates to function in this case (but we need to make sure to return them as outputs to Scan's inner function), can we just not return them at all to simplify the interface further?

Related to #101

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Attention: Patch coverage is 86.66667% with 4 lines in your changes missing coverage. Please review.

Project coverage is 98.03%. Comparing base (64b0e50) to head (fd670d5). Report is 19 commits behind head on main.

Files	Patch %	Lines
aemcmc/utils.py	80.00%	1 Missing and 3 partials :warning:

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[rlouf]

Decisions regarding the output format will be informed by the constraints that a general-purpose sampling function imposes.

Here are some thoughts:

• Returning a list is certainly the easiest, but it is also more cumbersome for the user;
• Returning a dictionary indexed by the random variables does not play well with downstream formats like XArray (to interface with ArviZ), and the random variables are not necessarily available to the user if the model is defined inside a function;
• Returning a dictionary indexed by variable name requires users to name variables. How do we handle missing names?

[dgerlanc]

• Returning a dictionary indexed by variable name requires users to name variables. How do we handle missing names?

We could automatically generate sequential names.

Alternatively, we return a list and provide another function(s) that generate other formats, dict, xarray

[brandonwillard]

We could automatically generate sequential names.

Definitely; and we can use the Variable.auto_name values for that.

Alternatively, we return a list and provide another function(s) that generate other formats, dict, xarray

Also a very viable approach!