Unified Measurement Framework: Bayesian Marketing Mix Modeling (MMM)

Objective: To establish a production-grade analytics pipeline that quantifying marketing impact using Bayesian inference and Causal Calibration.

About the Author

Samkit Shah | Master of Data Science Graduate (Monash University) & Marketing Technology Professional

"Bridging the gap between Media Strategy and Bayesian Statistics."

With 3 years of experience at Publicis Global Delivery managing large-scale campaigns and a rigid academic foundation in Data Science, I built this project to solve the industry's biggest challenge: Measurement in a Privacy-First World.

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The Problem: The "Attribution Crisis"

Digital marketing measurement is broken.

• Privacy Changes: iOS 14+ and cookie deprecation have rendered deterministic tracking (MTA) unreliable.
• Walled Gardens: Facebook and Google grade their own homework, often over-claiming credit.
• The Blind Spot: Traditional models ignore the "invisible" impact of brand building (TV, Viral TikToks) that doesn't result in an immediate click.

The Solution? Moving away from user-level tracking to Top-Down Statistical Modeling.

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System Architecture: The "Unified" Approach

We don't just run a regression; we build a Production-Grade Pipeline mirroring a modern Lakehouse architecture.

graph TD
    subgraph Ingestion
    A["Raw Data Sources<br/>(FB, Google, Shopify)"] -->|Ingest| B[("Bronze Layer<br/>Raw CSVs")]
    end

    subgraph "Data Engineering (Spark/Pandas)"
    B -->|Clean & Validate| C[("Silver Layer<br/>Cleaned Data")]
    C -->|Feature Eng<br/>Adstock & Saturation| D[("Gold Layer<br/>Modeling Ready")]
    end

    subgraph "Modeling (PyMC-Marketing)"
    D --> E["Bayesian MMM Model"]
    F["Industry Priors"] --> E
    G["Geo-Lift Experiment<br/>(Calibration)"] -->|Informative Prior| E
    end

    subgraph "Decisioning"
    E --> H["Posterior Distributions"]
    H --> I["Budget Optimizer"]
    I --> J["ROI Insights"]
    end

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Bayesian Technical Appendix: Why PyMC?

Why use Bayesian Inference instead of standard Machine Learning (Regression/Gradient Boosting)?

1. Prior Knowledge: We can mathematically encode industry expertise (e.g., "TV effects last longer than Social effects") using Priors.
2. Uncertainty Quantification: Instead of a single "ROAS" number, we get a Posterior Distribution, telling us the probability of an outcome (e.g., "There is a 95% chance TikTok ROI is between 2.5 and 3.1").
3. Small Data Resilience: MMM datasets are small (3 years = ~150 weekly points). Deep Learning overfits; Bayesian methods robustly handle uncertainty.

Core Tech Stack: PyMC, PyMC-Marketing, ArviZ, Pandas, Matplotlib.

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Executive Summary

This project answers the critical question: "Where should the next $1M be spent?"

Key Capabilities:

1. Ingestion: Robust pipelines for cross-channel data.
2. Calibration: Integrating "Ground Truth" from Geo-Lift experiments to unbias the model.
3. Optimization: Budget allocation algorithms to maximize Revenue/ROI under constraints.

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Getting Started

Prerequisites

• Python 3.10+
• Recommended: High-performance environment for MCMC sampling.

Installation

pip install .

Usage

Follow the pipeline to replicate the analysis:

1. Generate Data:

   python src/data_engineering/generate_synthetic_data.py

   Creates data/bronze/beauty_brand_mmm.csv

2. Process Data (Medallion Architecture):

   python src/data_engineering/process_silver.py
   python src/data_engineering/process_gold.py

   Enginners features (Adstock/Saturation) -> data/gold/

3. Train Bayesian Model (ADVI):

   python src/modeling/train_model.py

   Trains the initial probabilistic model using Variational Inference.

4. Run Geo-Experiment (Calibration):

   python src/modeling/simulate_geo_experiment.py
   python src/modeling/calibrate_model.py

   Simulates a Melbourne lift test and retrains the model with the new "Ground Truth" prior.

5. Optimize Budget:

   python src/modeling/budget_optimizer.py

   Outputs the optimal media mix recommendations.

Key Results

Optimization Opportunity: Found $83,713 (+4.8%) in daily revenue lift by reallocating budget.

Channel	Action	Rationale (Data-Driven)
TikTok	Cut 50%	Geo-Experiment revealed ROAS (3.5) was lower than Modeled (5.2).
Google	Boost 50%	capturing high-intent demand; S-Curve analysis shows room to scale.
FB	Boost 39%	Strong visual driver with efficient CPA.

Project Structure

• data/: Medallion architecture storage.
• src/: Source code.
  • data_engineering: ETL and Feature Engineering.
  • modeling: PyMC models, Simulation, and Optimization logic.
• reports/: Executive summaries and debugging logs.
• notebooks/: Exploratory analysis.