Add Bass Diffusion Model

[williambdean]

Description

Adding Bass Diffusion Model

Related Issue

• Closes Add Bass Diffusion Model #1126
• Related to #

Checklist

• Checked that the pre-commit linting/style checks pass
• Included tests that prove the fix is effective or that the new feature works
• Added necessary documentation (docstrings and/or example notebooks)
• If you are a pro: each commit corresponds to a relevant logical change

Modules affected

• MMM
• CLV
• Customer Choice
• Product Development

Type of change

• New feature / enhancement
• Bug fix
• Documentation
• Maintenance
• Other (please specify):

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📚 Documentation preview 📚: https://pymc-marketing--1328.org.readthedocs.build/en/1328/

[williambdean]

Here is a crude implementation of the Bass model. Feel free to take over @juanitorduz

I forget why I didn't wrap it in the ModelBuilder. Maybe I was just trying it out and familiarizing myself with the model. Maybe it will be straight forward but I remember having some concern.

As for the magnitude of m compared to the other parameters and NUTS, maybe a scaling constant can be used in the model. You might have some more ideas.

model = Bass(m_scaling=5000)

# Under the hood
m = m_scaling * Prior.create_variable(...)

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 93.55%. Comparing base (a87f1fa) to head (2a4dd03).
Report is 2 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1328      +/-   ##
==========================================
+ Coverage   93.53%   93.55%   +0.02%     
==========================================
  Files          55       56       +1     
  Lines        6357     6381      +24     
==========================================
+ Hits         5946     5970      +24     
  Misses        411      411              

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[juanitorduz]

Thanks @wd60622 ! I will familiarize myself with the model and push it forward 🙌

[williambdean]

Sounds good! Thanks

I had the idea we could parameterize it as days/weeks/months from product launch making pooling across dims / products easier. I feel like that would be an interesting insight.

[williambdean]

Visual produced from the main block:

[juanitorduz]

I will pick up this one so that we can merge the base model and iterate

[williambdean]

The magnitude of m might benefit from VariableFactory protocol allows for:

import pymc as pm
from pymc_marketing.prior import Prior

class Scaled: 
    def __init__(self, dist: Prior, factor: str): 
        self.dist = dist
        self.factor = factor 

    @property 
    def dims(self): 
        return self.dist.dims

    def create_variable(self, name: str): 
        var = self.dist.create_variable(f"{name}_unscaled")
        return pm.Deterministic(name, var * self.factor, dims=self.dims)

This would keep the model itself free from this scaling logic but still allow if needed.

from pymc_marketing.prior import sample_prior

m = Scaled(Prior("HalfNormal", sigma=1), 5000)
prior = sample_prior(m)