Hierarchical distributions for all parameters in model config

[wd60622]

The _create_likelihood_distribution accepts a nested dictionary. i.e.

pymc-marketing/pymc_marketing/mmm/delayed_saturated_mmm.py

Lines 540 to 545 in b763c12

	"likelihood": {
	"dist": "Normal",
	"kwargs": {
	"sigma": {"dist": "HalfNormal", "kwargs": {"sigma": 2}},
	},
	},

That is based on the single recursive section of that method

It might be beneficial to allow this nesting for other parameters in the model. For example, a spin on the current gamma_control can be viewed as hierarchical parameters for the control coefficients. Where the "gamma_control_mu" and "gamma_control_sigma" are then scaler population parameters for "gamma_control"

model_config = {
    ..., 
    "gamma_control": {
        "dist": "Normal", 
        "kwargs": {
            # "mu": 0,
            "mu": {"dist": "Normal", "kwargs": {"mu": 0, "sigma": 1}}, 
            # "sigma": 2, 
            "sigma": {"dist": "HalfNormal", "kwargs": {"sigma": 1}}, 
        }, 
        # Implicit in the model to have dims=control but could be explicit as well
        # "dims": "control"
    }, 
    ..., 
}

Overall, think it would be easy to add and would consolidate the model_config logic in the process.
Open to other's thoughts

[ColtAllen]

I've been wanting to nest distributions on the CLV side because Beta priors benefit from a pooled approach:

https://discourse.pymc.io/t/prior-distribution-for-certainty-parameter-of-beta-distribution/1071

However, as-written _create_likelihood_distribution doesn't support Beta distributions.

[wd60622]

I've been wanting to nest distributions on the CLV side because Beta priors benefit from a pooled approach:

https://discourse.pymc.io/t/prior-distribution-for-certainty-parameter-of-beta-distribution/1071

However, as-written _create_likelihood_distribution doesn't support Beta distributions.

Good to know. Thanks for the link

Can you point out where you had this in mind in clv module for reference.

Will Beta be the only likelihood you use? Or do they overlap with the mmm likelihood stored in that method?

In my mind, there will be some overlap in functionality so itd make sense to at least pull out the method into function. Then maybe have two separate main functions if needed

[ColtAllen]

Can you point out where you had this in mind in clv module for reference.

BetaGeoModel, ShiftedBetaGeoModelIndividual, and the upcoming BetaGeoBetaBinomModel all require Beta distributions.

Will Beta be the only likelihood you use? Or do they overlap with the mmm likelihood stored in that method?

Pooling distributions like Pareto and Uniform would also be needed. I used both in my fork of lifetimes:

https://github.com/ColtAllen/btyd/blob/main/btyd/models/beta_geo_model.py#L110

This was the only way I could get the MCMC posterior means to match the MLE results from research during testing. Right now BetaGeoModel will return very different parameter estimates for MAP/MCMC.

In my mind, there will be some overlap in functionality so itd make sense to at least pull out the method into function. Then maybe have two separate main functions if needed.

Could also move create_likelihood_distribution into the base ModelBuilder class so it's supported across the library.

[juanitorduz]

Yes! This would be great indeed!