Skip to content

IAI Actuarial Core Principles · Actuarial Statistics · Bayesian inference: priors, posteriors, loss functions and credible intervals

Which statement about a 95% Bayesian credible interval (a, b) for θ is correct?

The correct statement is that the posterior probability of θ lying between a and b, given the data, is 0.95. This is a direct probability statement about the parameter, unlike the repeated-sampling meaning of a confidence interval.

  1. AGiven the data and prior, P(a < θ < b | data) = 0.95Correct
  2. BIn repeated sampling, 95% of such intervals contain the fixed true θ
  3. CIt is always identical to the classical confidence interval
  4. DIt must be symmetric about the posterior mean
  5. The probability is conditional on θ, not on the data

Explanation

A credible interval is a direct posterior probability statement about θ given the data. The repeated-sampling statement is the confidence interval interpretation. Credible intervals need not be symmetric.

Did you get it right without looking?

One question tells you little. A timed set on Bayesian inference: priors, posteriors, loss functions and credible intervals shows your real accuracy, how long you take and where you lose marks.

Practise Bayesian inference: priors, posteriors, loss functions and credible intervalsFree diagnostic mock

More Bayesian inference: priors, posteriors, loss functions and credible intervals questions