Credible interval vs confidence interval.

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Answer

$CI (frequentist): 'if we repeated the experiment many times, 95% of these intervals would contain θ' — probability statement about the procedure.$
$P({\theta}\; \in \;[a, \;b]\; \mid \;\mathrm{data})\; = \;95$
$Numerically they can coincide with uninformative priors and large n, but they answer different questions.$
$Users usually want the credible interval interpretation.$

Check yourself — multiple choice

Same thing
CI: about the procedure across repetitions; credible: $P({\theta}\; \in \;[a, b]\; \mid \;\mathrm{data})$ — Bayesian statement about θ; numerically close under uninformative priors and large n
Only Bayesian is right
Only frequentist

CI: about the procedure; credible: about θ given data + prior.

#confidence-interval#bayesian

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