Bayesian priors

Why they exist: marketing data is small. Two years of weekly data is 104 observations, from which the model must estimate dozens of parameters. Pure data-driven estimation at that sample size produces absurdities, negative TV effects, ROIs of 40. Priors keep estimates in the physically plausible range, which is legitimate and necessary.¹ Meridian goes further and treats priors as the interface for calibration: run a geo experiment, get a measured lift, encode it as an informative ROI prior, and the model is now anchored to experimental truth.²

Why vendors argue: a flat prior says "let the data speak" and accepts noise; an informative prior says "we know things" and risks importing someone else's assumptions about your business. Both positions are defensible. What is not defensible is the abuse case: priors tight enough that the posterior is the prior wearing a data costume. Set TV's ROI prior to a narrow band around 2.0 and the model will dutifully report TV ROI near 2.0 regardless of what your revenue did. The output looks like measurement; it is transcription.

What to ask on the call, verbatim: "Which priors are informative, what informed them, and what does the posterior look like against the prior for my top three channels?" A good vendor shows posteriors that visibly moved away from priors, proof the data spoke. A vendor who cannot show prior-versus-posterior plots is asking you to trust the thumb. The full script lives in the 12 vendor questions.