pymc-marketing 0.0.2

Marketing Statistical Models in PyMC

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.

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"

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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

	Non-contractual	Contractual
Continuous	Buying groceries	Audible
Discrete	Cinema ticket	Monthly or yearly subscriptions

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.

Below are links to notebooks we've written that outline CLV models by type

Continuous non-contractual models

[links to notebook(s) here]

Continuous contractual models

[links to notebook(s) here]

Discrete non-conntractual models

[links to notebook(s) here]

Discrete contractual models

[links to notebook(s) here]

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Local Development

1. Create conda environment. For example:

conda create -n pymmmc_env python=3.8

2. Activate environment.

conda activate pymmmc_env

3. Install pymmmc 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