PyMC-Marketing

Bayesian Media Mix Models (MMMs) in PyMC

In this package we provide an API for a Bayesian media mix model (MMM) specification following Jin, Yuxue, et al. “Bayesian methods for media mix modeling with carryover and shape effects.” (2017).. Concretely, given a time series target variable $y_{t}$ (e.g. sales on conversions), media variiables $x_{m, t}$ (e.g. impressions, clicks or costs) and a set of control covariates $z_{c, t}$ (e.g. holidays, special events) we consider a linear model of the form

$$ y_{t} = \alpha + \sum_{m=1}^{M}\beta_{m}f(x_{m, t}) + \sum_{c=1}^{C}\gamma_{c}z_{c, t} + \varepsilon_{t}, $$

where $\alpha$ is the intercept, $f$ is a media transformation function and $\varepsilon_{t}$ is the error therm which we assume is normally distributed. The function $f$ encodes the contribution of media on the target variable. Typically we consider two types of transformation: adstock (carry-over) and saturation effects.

Here you can find a simulated example:

1. First, we describe the data genaration process of a simulated dataset.
2. Next, we describe how to specify and fit a media mix model (as described above) using the pymc-marketing MMM's API.
3. Finally, we describe the model results: channel constribution and ROAS estimation. We also show how the model recovers the parameters from the data generation process step.

References:

• Jin, Yuxue, et al. “Bayesian methods for media mix modeling with carryover and shape effects.” (2017).
• PyMC Labs Blog:
  • Bayesian Media Mix Modeling for Marketing Optimization
  • Improving the Speed and Accuracy of Bayesian Media Mix Models
• Johns, Michael and Wang, Zhenyu. "A Bayesian Approach to Media Mix Modeling"
• Orduz, Juan. "Media Effect Estimation with PyMC: Adstock, Saturation & Diminishing Returns"

Bayesian CLVs in PyMC

Customer Lifetime Value models is another important class of models. There are many different types of CLV models and it can be helpful to conceptualise them as fitting in a 2-dimensional grid as below. An excellent set of introduction slides to CLV's is provided in Probability Models for Customer-Base Analysis by Fader & Hardie (2009).

Examples

To explain further:

• Contractual: In contractual settings a customer has a contract which continues to be active until it is explicitly cancelled. Therefore in contractual settings, customer churn events are observed.

• Non-contractual: In non-contractual settings, there is no ongoing contract that a customer has with a company. Instead, purchases can be ad hoc and churn events are unobserved.

• Discrete: Here, purchases are made at discrete points in time. This obviously depends upon the timescale that we are working on, but typically a relevant time period would be a month or year. However it could be more granualar than this - think of taking the 2nd of 4 inter-city train journeys offered per day.

• Continuous: In the continuous-time domain, purchases can be made at any point within a firms opening hours. For online ordering this could be any point within a 24 hour cycle, or purchases in physical stores could be made at any point during the trading day.

In the documentation we provide some examples on how to use the CLV API. We use the data from the lifetimes package Quickstart section to illustrate the models.

• BG/NBD model
• Gamma-Gamma model

Local Development

1. Create conda environment. For example:

conda create -n pymc_marketing_env

2. Activate environment.

conda activate pymc_marketing_env

3. Install pymc_marketing package:

make init

4. To run tests:

make test

5. To check code style:

make check_lint

6. Set pre-commit hooks (Optional):

pre-commit install