Bayesian statistics uses Bayes rule to update beliefs about uncertain quantities within a probabilistic model. Bayes rule follows from conditional probability and the chain rule; Bayesianism gives those probabilities an interpretation as the modeler's uncertainty about an incompletely known data-generating process. section 2.1.4 section 2.4.2
The approach supports several stages of probabilistic causal work: Bayesian parameter estimation during training, probabilistic inference during causal analysis, and Bayesian decision theory for causal decisions. It therefore connects probability laws to models, computation, and decisions rather than treating Bayes rule as an isolated formula. section 2.4 section 2.1.4
A Bayesian model relies on a small set of connected probability concepts:
- Factor joint distributions with the chain rule, reducing one complex probability object to conditional factors that can be modeled separately. section 2.1.4
- Marginalize variables with the law of total probability, using summation for discrete variables and integration for continuous variables. section 2.1.4
- Represent uncertainty with distributions whose parameters may include location, scale, rate, and shape, while independence assumptions simplify the model. section 2.5
From physical randomness to model uncertainty
A die roll can be described as a repeatable physical process, but Bayesian probability also models phenomena such as speech production or climate-driven changes in ocean currents. In both cases, modeled probabilities express incomplete knowledge rather than necessarily inherent randomness in the underlying process. section 2.4.2
