Short answer
Bayesian MMM is Marketing Mix Modelling built on Bayesian statistics: the model is fit with prior beliefs about each parameter (informed by experiments and prior knowledge) and returns full probability distributions instead of single point estimates. It handles uncertainty, small data and calibration far better than the frequentist MMM of the 2000s.
Frequentist MMM asks 'what parameter values best fit the data?' Bayesian MMM asks 'given the data and what I already believed, what is the probability distribution over each parameter?' The output is a posterior distribution for every coefficient, ROI and saturation curve - not a single number.
Marketing data is short, correlated and noisy. Pure frequentist fits often produce unstable or economically silly coefficients (negative TV ROI, saturation curves that never saturate). Priors, informed by incrementality tests and industry knowledge, anchor the model in reality while still letting the data update the estimates.
Instead of 'TV ROI is 2.3', you get 'TV ROI is 90% likely to be between 1.8 and 2.9, with a most-likely value of 2.3'. That uncertainty flows into budget optimisation, scenario planning and risk-adjusted recommendations. Google's Meridian and Meta's Robyn are both Bayesian; PyMC-Marketing is the open-source standard.
Bayesian MMM is more computationally expensive (MCMC or variational inference rather than OLS), and it requires more judgement about prior choice. Done well, that judgement is a feature - it forces experiments and domain knowledge into the model. Done badly, priors become a way to smuggle in whatever answer you wanted.
Bayesian MMM, calibrated with experiments, refreshed monthly, delivered as a decision system.
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