Lesson 13 of 14 · All lessons in this module
  1. Random variables: PMF, PDF and CDF
  2. Expected value, variance and standard deviationVideo lesson
  3. Variance and covariance shortcuts, and the law of large numbers
  4. Discrete distributions: uniform, binomial and Poisson
  5. Continuous uniform and normal distributions, and simulating random draws
  6. Log-normal and logistic distributions, and the moments of key distributions
  7. Integrated cases: reading probabilities and moments from a return model
  8. Conditional probability and probability trees
  9. Conditional expected values and variancesVideo lesson
  10. Covariance from a joint probability function
  11. Joint, marginal and conditional distributions as information arrives
  12. Bayes' formula: updating a probability with new informationVideo lesson
  13. Bayes in practice: diffuse priors, missing inputs and screening tests
  14. Integrated cases: a tree with model forecasts and a Bayes update

This lesson is part of the 2027 curriculum. You are following the 2026 curriculum, where it is not taught in this form. Switch if you are sitting the exam under the 2027 curriculum.

Lesson 13 of 14 · 14 min

Bayes in practice: diffuse priors, missing inputs and screening tests

Exam Bayes problems usually hide one input: you may need to back it out with the total probability rule, use complements, or start from equal (diffuse) priors.

In short

  • When P(B)P(B) is given directly, Bayes is one line: P(A∣B)=[P(B∣A)/P(B)]×P(A)P(A \mid B) = [P(B \mid A)/P(B)] \times P(A).
  • If a likelihood is missing, solve for it with the total probability rule.
  • Complements help: P(fail∣S)=1−P(pass∣S)P(\text{fail} \mid S) = 1 - P(\text{pass} \mid S) and P(fail)=1−P(pass)P(\text{fail}) = 1 - P(\text{pass}).
  • A diffuse prior gives every event equal probability, so the posterior is driven entirely by the likelihoods.
  • Information is useful when it moves the posterior well away from the prior.

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