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Lesson 12 of 12 · 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 $P(B)$ is given directly, Bayes is one line: $P(A \mid B) = [P(B \mid A)/P(B)] \times P(A)$ .
If a likelihood is missing, solve for it with the total probability rule.
Complements help: $P(\text{fail} \mid S) = 1 - P(\text{pass} \mid S)$ and $P(\text{fail}) = 1 - P(\text{pass})$ .
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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