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## Marketing Science Seminar (Track B)

### Marketing Mix Modeling and Optimization with Bayesian Networks & BayesiaLab

**September 28, 2016, 9:30 a.m. – 4:30 p.m. ****Schermerhorn Symphony Center, One Symphony Place, Nashville, TN 37201**

Note: This seminar is part of the main program of the 4th Annual BayesiaLab Conference.

## Overview

Our marketing science seminar consists of a morning and afternoon session, which run approximately two hours each. The morning session focuses on fundamental causal questions, such as how to estimate causal effects from observational data. In the afternoon, we apply these concepts to the field of marketing science. More specifically, we build a Bayesian network model for marketing mix optimization. In this context, we also introduce a new method for estimating contributions using counterfactuals.

Between the sessions, we'll take a one-hour lunch break.

## Motivation & Background

**“Half the money I spend on advertising is wasted;**

**The trouble is I don’t know which half.”**

Over the last century, various versions of this quote have been attributed to John Wanamaker, Henry Ford, and Henry Procter, among others. Yet 100 years after these marketing pioneers, in this day and age of big data and advanced analytics, the quote still rings true among marketing executives. The ideal composition of advertising and marketing efforts remains the industry's Holy Grail. The current practice remains “more art than science.” The lack of a well-established marketing mix methodology has little to do with the domain itself. Rather, it reflects the fact that marketing is yet another domain that typically has to rely on non-experimental data for decision support.

## Morning Session (10:00 AM – 12:00 PM)

### It's a Causal Question!

The single most important thing we need to recognize about marketing mix modeling is that it is a causal question. This means we are not looking for a prediction of an outcome variable based on the observation of marketing variables. Rather, we are attempting to manipulate the available marketing variables to optimize the outcome. Thus, we must simulate interventions, not observations, and we must switch from observational inference to causal inference. This brings us to the Holy Grail of statistics, i.e. deriving causal inference from observational data. Is this even possible?

### Graphical Models for Causal Identification

We introduce the fundamental concepts of probabilistic graphical models and how they can help us perform causal identification, i.e. determine whether or not it is possible to estimate a causal effect from observational data. For this, we require causal assumptions about the domain (from expert knowledge) plus a decision criterion, such as the well-known **Adjustment Criterion**. While it is straightforward in theory, the complexity of the marketing domain limits the practical application of this criterion. As an alternative, we introduce the **Disjunctive Cause Criterion** (Shpitser and VanderWeele, 2011) that significantly reduces the number of assumptions required for causal identification and, consequently, confounder selection. In theory, we now have all we need to estimate causal effects. In practice, it is only half the battle.

## Afternoon Session (1:00 PM – 3:00 PM)

### Bayesian Networks and BayesiaLab

To go from causal identification to causal effect estimation, we require an "inference engine." In the simplest case, we could use a regression. However, with dozens of interacting variables, that is no longer feasible. This is where **Artificial Intelligence** comes into play: we employ the machine-learning algorithms of the BayesiaLab software platform, which can build a high-dimensional statistical model that represents the joint probability distribution of all marketing variables. As a result, we obtain a Bayesian network that represents a multitude of relationships between drivers and the outcome variable. Using BayesiaLab’s visualization tools, we compare the machine-learned graph to our understanding of the domain. Furthermore, we can examine the (mostly nonlinear) response curves of the outcome variable as a function of the marketing drivers. Most importantly, we use BayesiaLab to perform **Likelihood Matching** on all confounders to establish the causal response of the outcome variable.

### Resources and Optimization

With all causal response curves computed, we introduce cost functions for each marketing driver via BayesiaLab’s **Function Node**. On that basis, we proceed to **Target Optimization**,** **which, by means of a genetic algorithm, searches for an optimal combination of all marketing drivers, while being subject to constraints of individual variables and an overall marketing budget constraint. The optimization report shows feasible solutions along with the degree of achievement.

### Counterfactuals and Contribution

The final step in developing our marketing mix model is the question of attribution and contribution. While it is easy to understand the meaning of "contribution," calculating a numerical value that represents this concept is not. We introduce counterfactuals as a necessary device to compute the contributions of individual marketing drivers.