Get in touch with our team
Feature image for 15.03.2024


3 min read

Bayesian Statistics in Media Mix Modelling: A real-world analogy

This article was updated on: 22.03.2024

Bayesian statistics is a powerful tool for tackling the complexities inherent in media effectiveness analysis, making it an attractive approach for practitioners in the field. Bayesian statistics particularly shines in media mix modelling (MMM) for its ability to incorporate prior knowledge and enhance model robustness with limited or missing data.

Additionally, Bayesian methods facilitate the handling of uncertainty, enabling more reliable inference and decision-making processes.

The Bayesian framework consists of three main components: the prior, the likelihood and the posterior.

In the context of MMM, the prior reflects any initial beliefs or assumptions on the model parameters before observing any data. The likelihood quantifies the probability of observing the data given the model’s prior. The posterior integrates the prior and likelihood, yielding “updated” beliefs after considering the observed data.

It is the posterior that contains all relevant insights for an informed decision-making process.

As an example, let us consider the task of predicting whether or not to wear a raincoat based on weather conditions. This can be modelled in a similar way to the digital marketer’s crucial challenge of allocating budgets for a campaign across various media channels.

Initial Uncertainty (Objective)Raincoat Scenario: You wake up and your curtains are closed, you can’t hear any rainfall initially. This tells you a little about the chance of rainfall, but not enough to decide whether or not to wear a raincoat.Marketing Campaign: You wish to launch a campaign but don’t have any insights into channel performance to help you decide which channels to advertise on.

Historical Beliefs (Prior)Raincoat Scenario: Based on previous years you think there is about a 40% chance of rainfall around this time of year.Marketing Campaign: You recall your knowledge of channel performance for previous campaigns and how budgets were allocated then.
Seeing the data (Likelihood)Raincoat Scenario: Upon looking outside you see the sky is overcast with dark, heavy clouds. The likelihood of needing a raincoat increases considerably, but not to certainty.Marketing Campaign: You update your campaign’s expected success using real-time data from various media channels.
Accounting for externalities (Externalities)Raincoat Scenario: You check a weather app on your phone, which factors in wind speeds and humidity, and see a 60% chance of rainfall in your area.Marketing Campaign: You decide to consider external factors that may impact the performance of your campaign, such as seasonality and consumer behaviour.
Decision-making insights (Posterior)Raincoat Scenario: Combining your historical beliefs with today’s observations and the weather forecasts, you estimate there is a 75% chance of needing a raincoat and deciding to wear one.Marketing Campaign: Through incorporating prior knowledge, historical data and externalities, the Bayesian MMM has produced an estimate of your optimal media mix and its associated probabilities. You choose to allocate budgets for the campaign this way.

To conclude, the increasing popularity of Bayesian statistics within media effectiveness measurement reflects a paradigm shift towards more robust and flexible frameworks. By leveraging Bayesian methods, marketers can better account for uncertainty, incorporate prior knowledge, and refine their insights, leading to more accurate and actionable marketing strategies.