Bayesian Inference Model Documentation
Causality Engine’s causal inference model quantifies incremental marketing impact by estimating channel effects with probabilistic reasoning, updating beliefs with observed data for robust attribution.
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By Joris van Huët, Founder & CEOUpdated 1 min read
Bayesian Inference Model Documentation
Causality Engine’s core attribution engine uses causal inference to estimate the incremental impact of marketing channels.
Likelihood Function
Assuming a generalized linear model:
P(Y | X, \theta) = f(\beta_0 + \sum_{i=1}^n \theta_i X_i)
where (f) is a link function (e.g., logistic for binary outcomes).
Prior Distribution
Priors (P(\theta)) encode initial beliefs about channel effects, typically Gaussian with mean zero and variance reflecting uncertainty.
Posterior Computation
Using Bayes theorem:
P(\theta | Y, X) \propto P(Y | X, \theta) \cdot P(\theta)
This posterior is approximated using Markov Chain Monte Carlo (MCMC) or Variational Inference for computational efficiency.
Incremental Impact Estimation
From the posterior distribution, we derive:
Posterior mean: Expected incremental impact per channel
Credible intervals: Uncertainty ranges for effect sizes
Handling Confounders
The model incorporates observed confounders (e.g., seasonality, promotions) as covariates to isolate channel effects accurately.
Practical Implications
Cannibalistic Detection: Identifies negative correlations among (\theta_i).
Mathematical Summary
\text{Posterior} = \frac{\text{Likelihood} \times \text{Prior}}{\text{Evidence}} = \frac{P(Y|X,\theta)P(\theta)}{P(Y|X)}
Related Resources
Frequently asked questions
What statistical model underpins Causality Engine’s attribution?
Causality Engine uses causal inference on the GA4 history you already have to estimate what each channel caused.How are channel effects interpreted in the model?
Each \(\theta_i\) represents the incremental lift attributable to channel \(i\), with uncertainty quantified by credible intervals.What inference methods are used for posterior estimation?
Markov Chain Monte Carlo (MCMC) or Variational Inference techniques approximate the posterior distribution.How does the model handle confounding factors?
Confounders are included as covariates to isolate the true causal effects of marketing channels.Can the model output be used for budget optimization?
Yes, posterior mean effects inform the Optimization Queue to prioritize channels by incremental ROAS.
Go deeper: Causal attribution, explained.
Sixty-second versions of these ideas: Causality Engine on YouTube Shorts.
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Terms in this article
- AttributionAttribution identifies user actions that contribute to a desired outcome and assigns value to each. It reveals which marketing touchpoints drive conversions.
- Bayesian InferenceBayesian Inference updates the probability of a hypothesis based on new evidence. It refines marketing attribution by incorporating prior beliefs about channel effectiveness.
- Causal InferenceCausal inference is the set of methods for estimating how much an outcome changes because of a cause, rather than alongside it. It works by comparing what happened with an estimate of what would have happened without the cause.
- CausalityCausality is the relationship where one event directly causes another, essential for identifying specific actions that drive desired outcomes in marketing.
- CorrelationCorrelation is a statistical measure showing a relationship between variables; it does not imply causation.
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