Bayesian Commercial Decision Engine: Google Meridian MMM, Probabilistic CLV & Distributed ML

Modern commercial decision engines require rigorous econometric modeling: Bayesian media attribution, probabilistic customer lifetime value, and cost-sensitive churn classification.

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📌 Executive Summary

Superficial marketing analytics relies on last-click attribution, heuristic customer segmentation, and uncalibrated churn alerts, generating massive capital misallocation.

This repository implements a four-tier quantitative marketing engineering framework bridging Bayesian econometrics, probabilistic customer modeling, and distributed machine learning.

Across a $10.1M media budget, the Bayesian optimization engine disproved naive ROAS metrics, unlocking +$419K in incremental revenue by reallocating spend from saturated channels to high-marginal-ROI drivers.

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🏛️ Analytical Framework Architecture

                    QUANTITATIVE MARKETING SUITE
                                 │
         ┌───────────────────────┼───────────────────────┐
         ▼                       ▼                       ▼
┌──────────────────┐    ┌──────────────────┐    ┌──────────────────┐
│  Bayesian MMM &  │    │  Probabilistic   │    │  Cost-Sensitive  │
│   Optimization   │    │   CLV Modeling   │    │  Churn Modeling  │
│(Project_colombini│    │ (HW2_fcolombini4)│    │(HW1 & HW3 Spark) │
└────────┬─────────┘    └────────┬─────────┘    └────────┬─────────┘
         │                       │                       │
         ▼                       ▼                       ▼
Google Meridian Bayesian  BG/NBD + Gamma-Gamma   Scikit-Learn & PySpark
Adstock & Hill Curves     14-Table FMCG Schema   Asymmetric Cost Matrix
mROI Budget Reallocation Survival Probabilities  Distributed Assembly
         │                       │                       │
         └───────────────────────┼───────────────────────┘
                                 ▼
                    EXECUTIVE DECISION REPORTS
         Vector Executive Presentations & Notebook Evidence

The codebase progresses from single-customer behavioral economics to enterprise-scale distributed data pipelines processing millions of interaction logs.

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🔬 Core Quantitative Modules

1. Bayesian Marketing Mix Modeling & Budget Optimization (Project_fcolombini4)

• Google Meridian Engine (Project_fcolombini4/src/modeling.py): Hierarchical Bayesian MMM incorporating Adstock decay, Hill saturation functions, and territory priors (UK and US).
• Marginal ROI Reallocation (Project_fcolombini4/src/optimization.py): Capital reallocation based on outputs/tables/optimization_results.csv. Cuts saturated Google Display spend by -44.4% while expanding Meta Facebook (+9.4%) and Meta Other (+50.0%).
• Model Explainability (Project_fcolombini4/src/shap_analysis.py): SHAP tree explanations deconstructing non-linear media channel interactions and seasonality across territories.
• Deliverables: Verified executive slide deck Project_fcolombini4/Project_Presentation.pdf and interactive analysis Project_fcolombini4/notebooks/mmm_homework.ipynb.

2. Customer Lifetime Value & BTYD Modeling (HW2_fcolombini4)

• Probabilistic Spend Engines (HW2_fcolombini4/HW2.py): Combines Beta-Geometric / Negative Binomial Distribution (BG/NBD) transaction processes with Gamma-Gamma monetary value modeling.
• Relational FMCG Database: Integrates 14 distinct enterprise entities documenting transactions, discounts, price changes, and support tickets via [HW2_fcolombini4/data/ER Diagram.md](HW2_fcolombini4/data/ER Diagram.md).
• Customer Segmentation: Calculates survival probabilities $P(\text{Active})$, expected transaction frequencies, and margin concentration curves.
• Deliverables: Methodological whitepaper HW2_fcolombini4/CLV_BG_NBG.pdf and executive deck HW2_fcolombini4/HW2_Presentation.pdf.

3. Cost-Sensitive Churn Prediction (HW1_fcolombini4)

• Asymmetric Loss Functions (HW1_fcolombini4/HW1_starter_code.py): Calibrates classification thresholds against true financial payoff matrices rather than arbitrary 0.5 cutoffs.
• Retention Trade-offs: Balances false-negative attrition damage against the commercial cost of unnecessary retention incentives.
• Deliverable: Technical evaluation report HW1_fcolombini4/HW1_ChurnPrediction.pdf.

4. Distributed Big Data Churn Pipeline with Apache Spark (HW3_fcolombini4)

• PySpark MLlib Architecture (HW3_fcolombini4/HW3_starter_code.py): Distributed feature extraction, VectorAssembler pipelines, and distributed gradient boosting.
• Strict Schema Enforcement: Validates input records against formal schemas via HW3_fcolombini4/schemas/dataset1_churn_schema.json.
• Deliverable: Distributed architecture deck HW3_fcolombini4/HW3_ChurnPredictionSpark.pdf.

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📊 Empirical Budget Optimization Matrix

Budget optimization results extracted from Google Meridian Bayesian model fit:

Channel	Historical Spend	Optimized Spend	Spend Delta	Historical Revenue	Optimized Revenue	mROI	Status
Google Display	$90,000	$50,000	-44.4%	$233,731	$184,774	1.65	Saturated / Cut
Meta Facebook	$7,460,000	$8,160,000	+9.4%	$24,745,710	$26,335,322	2.21	Under-invested
Meta Instagram	$2,530,000	$1,850,000	-26.9%	$5,275,156	$4,131,028	1.79	Rebalanced
Meta Other	$20,000	$30,000	+50.0%	$106,339	$129,128	2.08	High Potential

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🛠️ Environment & Reproduction

Each module maintains isolated execution scripts and dependencies:

# 1. Marketing Mix Modeling (Google Meridian)
cd Project_fcolombini4
pip install -r requirements.txt
python src/modeling.py

# 2. Customer Lifetime Value (BTYD / Lifetimes)
cd ../HW2_fcolombini4
python HW2.py

# 3. Apache Spark Churn Pipeline
cd ../HW3_fcolombini4
spark-submit HW3_starter_code.py

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Author: Francesco Colombini
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