How Bayesian priors keep your MMM honest when data is thin

Marketing mix models have a dirty secret: with 150 weeks of data and 12 channels, there are many wildly different stories the numbers can support. A frequentist model picks one and presents it with a straight face. A Bayesian model admits the ambiguity - and lets you constrain it with things you already know.

What a prior actually is

A prior is a statement of plausible ranges before the model sees your data. Not a guess at the answer - a fence around the absurd:

• Ad spend does not reduce sales, so channel effects are non-negative.
• A channel rarely returns 40x, so ROI beyond that needs overwhelming evidence.
• TV adstock decays over weeks, not hours.

These sound obvious. That is the point. Without them, thin data plus flexible models produces confident nonsense - a paid social coefficient of zero one quarter and a hero number the next.

Priors are not cheating

The common objection is that priors bias the result toward what you already believe. Two answers:

1. Weak, wide priors only rule out the impossible. Strong data overrules them; thin data gets stabilised by them. That trade is exactly what you want.
2. The alternative is not "no assumptions" - it is hidden assumptions baked into model structure that nobody reviews. Priors put the assumptions on the table where your team can argue with them.

Calibrating with experiments

The best priors come from your own experiments. A geo-holdout test on Meta gives you a measured incrementality range - feed it in as a prior and the model is now anchored to ground truth rather than folklore. Each experiment you run tightens the fence a little more.

A model without priors is not neutral. It is just uncalibrated.

If your MMM vendor cannot show you the priors, ask what is holding the model up instead. The answer is usually "the optimiser's imagination".