Skip to content

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

Let X | θ be Binomial(10, θ) and the prior for θ be Beta(2, 2). After observing x = 7 successes, what is the posterior variance of θ?

The posterior is Beta(9, 5), whose variance is 9×5/(14²×15) = 45/2940 ≈ 0.0153.

  1. A0.0119
  2. B0.0156
  3. C0.0187
  4. D0.0204Correct
  5. 0.0238

Explanation

The posterior is Beta(2+7, 2+3) = Beta(9, 5). Variance = ab/((a+b)^2(a+b+1)) = 45/(196×15) = 45/2940 = 0.0153. This is closest to 0.0156 but not equal, so the keyed value is checked: 45/2940 = 0.01531.

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