A prior probability distribution represents beliefs about unknown quantities before observing the relevant data. In Bayesian estimation, those quantities are model parameters, treated as random variables rather than fixed values. section 2.3.4
A prior has hyperparameters that the modeler specifies. Combining the prior with observed variables produces a posterior distribution: an entire distribution, or samples representing it, rather than a single parameter estimate. section 2.3.4
The practical role of a prior is to make uncertainty and prior knowledge explicit:
- It expresses subjective beliefs about plausible parameter values before data are incorporated. section 2.3.4
- It supports uncertainty-aware predictions and other inferences by preserving a distribution over parameter values. section 2.3.4
- It can constrain causal discovery by favoring or excluding graph structures, such as required or forbidden edges. section 4.6.1
Causal graph discovery
When searching a large space of possible directed acyclic graphs, prior knowledge can specify edges that must be present or absent, or impose Bayesian priors on graph structure. section 4.6.1
