concepts:
  - id: prior
    title: Prior
    description: A probability distribution representing knowledge before evidence.
    prerequisites: []
    mastery_signals:
      - explain a prior distribution
      - compare reasonable priors
    mastery_profile:
      template: bayes_concept

  - id: posterior
    title: Posterior
    description: Updated beliefs after conditioning on observed evidence.
    prerequisites:
      - prior
    mastery_signals:
      - explain updating beliefs
      - compare prior and posterior distributions
    mastery_profile:
      required_dimensions:
        - correctness
        - explanation
        - transfer
        - critique
      dimension_threshold_overrides:
        critique: 0.78