Using a random variable as observed

Questions
5

I have two ideas on how to trick pymc3 into using an observed variable as observed, I am not sure if it’s a good idea though. It may also be important to note that if PyMC3 were to allow random variable as observed, that would break after sampling when trying to convert to ArviZ and compute convergence chechs.

Option 1

Use a pm.Potential. I believe something like pm.Potential("wpp", pm.Beta.dist(alpha=alpha, beta=beta).logp(raw_with_slight_adjustment)) will add the right term to the joint probability.

Option 2

Use the cursed DensityDist. There are at least 5 options to do that with a densitydist, 3 of which should work in this situation, afaik, all 5 should work when using proper observed values (and many won’t need the density_dist_obs thingy when doing so). Remember to use idata_kwargs={"density_dist_obs": False}

2.1
DensityDist(
    "wpp", 
    pm.Beta.dist(alpha=alpha, beta=beta).logp, 
    observed=raw_with_slight_adjustment
)

This won’t work because if observed is not a dict, DensityDist has the same check all other distributions do, and doesn’t allow FreeRVs to be passed.

2.2
DensityDist(
    "wpp", 
    pm.Beta.dist(alpha=alpha, beta=beta).logp, 
    observed={"value": raw_with_slight_adjustment}
)

This should now trigger the dict checks, and avoid the FreeRV one. I still don’t know if this is a feature or a bug, at the very least feels wrong to me. One can see in the docs that the logp method of beta takes a value argument, so this should be public knowledge, what I don’t think is documented anywhere official is the array vs dict input trick. I have lost count of how many discourse posts and issues I have answered explaining that and saying density_dist_obs=False should be used.

2.3
DensityDist(
    "wpp", 
    lambda a, b, raw: pm.Beta.dist(alpha=a, beta=b).logp(raw), 
    observed={"raw": raw_with_slight_adjustment, "a": alpha, "b": beta}
)
2.4
def logp_fun(raw):
    pm.Beta.dist(alpha=alpha, beta=beta).logp(raw)
pm.DensityDist("wpp", logp_fun, observed=raw_with_slight_adjustment)

Again, won’t work because no dict input

2.5
def logp_fun(raw):
    pm.Beta.dist(alpha=alpha, beta=beta).logp(raw)
pm.DensityDist(
    "wpp", logp_fun, observed={"raw": raw_with_slight_adjustment}
)

Disclaimer: I don’t have the slightest idea of which of these approaches is the one DensityDist was designed for, if there are any differences between them when it comes to preformance nor if one of these (or a 6th alternative) should be the “recommended” approach. I personally prefer the Potential option, but this opinion is only based on style and conceptual coherence in the use of observed

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