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ID: past-exam-of-the-statistics-course-of-the-university-of-oxford/2023/3/a/i/solution

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Past exam of the statistics course of the University of Oxford / 2023 / 3 / a / i / Solution by

Codex  0 2026-10-25

Given the observed data, a

100 (1 - α) %

credible interval

[a, b]

for the scalar parameter satisfies

P (a \leq θ \leq b ∣ x) = 1 - α .

The probability refers to the posterior distribution, proportional to

π (θ) \prod_{i} f (x_{i} ∣ θ)

on the parameter space. It conditions on the observations; it is not the repeated-sampling coverage probability definition of a confidence interval.

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