Question: BART with Binomial liikelihood?

[juanitorduz]

Hi! 👋 ! I am trying to use a BART to model a Binomial likelihood as

with pm.Model() as model:
    mu = pmb.BART(name="mu", X=x, Y=k)
    p = pm.Deterministic(name="p", var=pm.math.invlogit(mu))
    pm.Binomial(name="likelihood", n=n, p=p, observed=k)

However I have problems sampling as the initial value of mu is very high and makes p=1.0. I tried changing the initval but Ii believe the problem is conceptual: According to https://bayesiancomputationbook.com/markdown/chp_07.html#the-bart-model The BART model works when modeling the expected value. For the normal, poisson, negative-binomial and Bernoulli this is fine as one of the parameters represents the mean. This is however not the case for a Binomial distribution Binomial(n, p) where the expected value is np. Do you have a tip or trick to use BART with a Binomial likelihood? Or am I missing something ini the model parametrization ?

Remark It seems the inv_link from BART is not available in pymc 5.0.1 right?

Thanks :)

[aloctavodia]

Hi,

I think this issue is not directly realted to BART and it can be solved by subtracting a small number to pm.math.invlogit(mu) or something fancier, like what we do in Bambi.

The original BART model and many of its variations and implementations model the expected value, and thus it is generally discussed in those terms. But the pymc_bart implementation is more flexible, and hence probably a better way to describe it is as a prior over step functions. With the support of such functions being the real line. This is true starting with PyMC 4, so we deprecated inv_link.

The goal of PyMC_BART is that it should work with any likelihood the user picks and any of its parameters. It should not be a problem to model p of the Binomial or sigma from a Normal... In practice, I think I have only tried with Normal, Student, Poisson, NegativeBinomial, Binomial, and Asymmetric Laplace.

[juanitorduz]

Thank you for the input! Much appreciated! I will try it out.
If you want you can close this issue ... or even better we could add a version of the second and third paragraph ("The original BART model ...") to the docs :). I think is a very useful remark.

[juanitorduz]

btw! it worked! I'll share the results once I clean them up! :)

[aloctavodia]

Great news. And thanks for asking and sharing. As we are still unsure of the practical limits and strengths of BART example, both when it works and when it doesn't, are much appreciated.

[juanitorduz]

Here you can find a first iteration of the simulated example: BART model with Binomial likelihood.