Methods appendix
How this model works, and where it stops working
Every number this tool reports comes out of one generative model fitted by MCMC. This section writes that model down in full — the likelihood, each prior, the transforms, and the algebra in between — so the output can be argued with rather than taken on trust. Each chapter ends by naming what it cannot do.
- 01The generative modelThe mean surface, the likelihood, and every prior on it — written out in full, because a model you cannot transcribe is one you cannot disagree with.
- 02Carryover and saturationAdstock then Hill, in that order, normalized so the decay parameter cannot quietly rescale the coefficient it multiplies.
- 03ROI is sampled, beta is derivedThe structural choice the rest of the engine hangs off: put the prior where a marketer has an opinion, and solve for the coefficient.
- 04What the data can identifyCollinearity after transformation, degrees of freedom, and baseline flexibility — the three ways an MMM returns your prior and calls it a finding.
- 05Priors and experiment calibrationEliciting a belief in ROI space, and the one route by which a lift test is allowed to become a prior.
- 06Geography and the baselineA non-centered geo hierarchy, a reference geo, and a knot spline deliberately coarser than the competition's.
- 07InferenceNUTS for anything quotable, mean-field SVI for iterating on priors, and why the distinction is carried on the artifact.
- 08Derived quantitiesAverage ROI, marginal ROI and contribution — each computed per draw, because the mean of a ratio is not the ratio of the means.
- 09Adversarial validationA scorecard that tries to break the fit: placebo channels, perturbed inputs, and a holdout graded against a benchmark that cannot see the future.
- 10Budget allocationReallocation against the stored posterior, reporting the probability a plan wins rather than a single optimistic number.