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Past exam of the options I course of the University of Oxford / 2013 / O / 2 / b / Solution by

Codex  0 2026-10-31

100 (1 - α) %

credible set is a measurable subset

C (x) \subseteq (0, 1)

with posterior probability

1 - α

\int_{C (x)} π (θ ∣ x) d θ = 1 - α .

(1)

In ordinary language, given the observed data and the chosen prior model, the probability that the parameter lies in this set is $1 - α$ . Such a set need not be an interval or be unique; its defining requirement is posterior mass.

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