Skip to content

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

A prior for a Poisson mean λ is Gamma(α=4, β=2) (rate β). A portfolio has 10 claims observed over 3 years of exposure so that the sample data give total count 10 with n = 3 observations. What is the posterior distribution of λ, from which a Bayesian credible interval would be built?

The posterior is Gamma(14, 5). With a Gamma prior and Poisson data, add the total count 10 to the shape 4 and the number of observations 3 to the rate 2. The credible interval is then read from this posterior distribution.

  1. AGamma(14, 5)Correct
  2. BGamma(14, 3)
  3. CGamma(10, 3)
  4. DGamma(7, 5)
  5. Gamma(4, 5)

Explanation

For Poisson data with a Gamma(α, β) prior, the posterior is Gamma(α + Σx, β + n) = Gamma(4+10, 2+3) = Gamma(14, 5). Gamma(14, 3) forgets to add the prior rate parameter to n and uses only n as the rate. Credible intervals are then taken from this posterior.

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