How to set a different prior distribution for the coefficient of each control variable

[mcb00]

I'd like to set the prior distribution for the coefficient of each control variable individually. For example, let's say I have two controls event_1 and event_2, and I'd like to set a Normal distribution on the coefficient for event_1 and a HalfNormal distribution for the coefficient of event_2. Is this supported somehow in the current API? If not any ideas about the easiest way to do it?

[williambdean]

You should be able to do this by following the VariableFactory protocol class. The MMM should just require the create_variable method

Here is some inspiration:

from pytensor import tensor as pt
import pymc as pm

from pymc_marketing.mmm import LogisticSaturation
from pymc_marketing.prior import Prior, sample_prior


class ConcatenatePrior:
    def __init__(
        self,
        first: Prior,
        n: int,
        second: Prior,
        dims: str,
    ):
        self.first = first
        self.n = n
        self.second = second
        self.dims = dims

    def create_variable(self, name: str):
        model = pm.modelcontext(None)

        coords = model.coords[self.dims]

        model.add_coords(
            {
                f"{self.dims}_first": coords[: self.n],
                f"{self.dims}_second": coords[self.n :],
            }
        )

        self.first.dims = f"{self.dims}_first"
        self.second.dims = f"{self.dims}_second"

        return pm.Deterministic(
            name,
            pt.concatenate(
                [
                    self.first.create_variable(name=f"{name}_first"),
                    self.second.create_variable(name=f"{name}_second"),
                ]
            ),
            dims=self.dims,
        )


variable = ConcatenatePrior(
    first=Prior("Normal"),
    n=2,
    second=Prior("HalfNormal"),
    dims="channel",
)

coords = {"channel": ["first", "second", "third", "fourth"]}
with pm.Model(coords=coords) as model:
    variable.create_variable("test")

    idata = pm.sample_prior_predictive()

idata.prior["test"].to_series().unstack().hist(sharex=True)
plt.show()

priors = {"beta": variable}
saturation = LogisticSaturation(priors=priors)
prior = saturation.sample_prior(coords=coords)
curve = saturation.sample_curve(prior)
saturation.plot_curve(curve)
plt.show()

You might run into some issues with I/O and have to implement the to_dict and from_dict methods for ModelBuilder constraints

pymc-marketing/pymc_marketing/model_builder.py

Lines 357 to 358 in dcbfa60

	if hasattr(x, "to_dict"):
	return x.to_dict()

Just doing the to_dict should allow you to fit the model.

[mcb00]

@williambdean thanks for the inspiration; this is helpful context for how these things are implemented in the MMM class.

[williambdean]

Awesome. Give it a try and let us know how it goes