Bayesian Marketing

A statistical approach to marketing budget allocation that uses Bayes' theorem to update probability estimates as new data arrives. Unlike traditional Marketing Mix Modeling which produces a single point estimate (e.g., 'Channel X delivers 3.2x ROAS'), Bayesian MMM produces a posterior distribution: a full range of probable outcomes with associated confidence levels. This allows marketers to make budget decisions based on the probability of exceeding a target, not just the expected value.

In Bayesian statistics, the prior distribution represents what you believe about an unknown quantity before seeing any data. In marketing, a prior distribution for a channel's ROAS might be set based on industry benchmarks or historical data from similar campaigns. The prior is updated with observed data to produce the posterior distribution.

The probability distribution of an unknown quantity after incorporating observed evidence. In the context of Bayesian MMM, the posterior distribution represents the updated probability that a given marketing channel will exceed a client's target return, after the model has processed all available historical data. The posterior distribution is what allows the Bayesian Brain to express budget recommendations as probabilities rather than point estimates.

The mathematical formula that describes how to update a probability estimate when new evidence is observed. The formula is: P(A|B) = P(B|A) × P(A) / P(B). In plain English: the probability of A given B equals the probability of B given A, multiplied by the probability of A, divided by the probability of B. In marketing, A is 'this channel will exceed target' and B is 'we observed these campaign results.'

The application of Shannon's information theory to marketing content strategy. Information theory measures the 'surprise value' or information content of a message: content that tells the reader something they did not already know has high information content, while content that restates common knowledge has low information content. Zennith uses entropy-based content scoring to identify which topics have the highest information value relative to what competitors have already published.

A measure of the average information content or uncertainty in a probability distribution, named after Claude Shannon. In the context of content strategy, Shannon entropy can be used to measure how much new information a piece of content adds to the existing corpus of published material on a topic. High-entropy content: content that is genuinely novel and informative: is more likely to be cited by AI engines than low-entropy content that restates existing knowledge.

A metric used in mathematical marketing optimisation that combines the expected reach of a campaign with the probability that the reached audience will take the desired action. ENR is maximised by allocating budget to channels that reach the highest-probability converters, not just the largest audiences. Zennith uses Stochastic Mixed-Integer Nonlinear Programming (MINLP) to maximise ENR under budget constraints.

A mathematical model of a system that transitions between states, where the probability of each transition depends only on the current state (not the history). In marketing, Markov chains model the customer journey: a prospect moves through states (Aware, Considering, Intending, Purchasing) with defined transition probabilities. Mixture of Markov Models (MOMM) extends this to model multiple distinct buyer archetypes simultaneously.

A concept from Game Theory where no player can improve their outcome by unilaterally changing their strategy, given the strategies of all other players. In marketing, Nash Equilibrium analysis identifies the stable state of a competitive market: the channel mix where no competitor can gain advantage by reallocating budget. Identifying channels where the market has not yet reached Nash Equilibrium reveals opportunities where a brand can gain disproportionate advantage.

The deliberate application of mathematical models, computational systems, and engineering principles to marketing strategy. Marketing Engineering treats marketing as a rigorous, quantitative discipline, using Bayesian inference, information theory, and game theory, rather than as a creative exercise. The central thesis of Zennith Agency's Mathification of Marketing: the agency that treats marketing as a mathematical system will always outperform the one that treats it as a creative exercise.