Skip to content

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

Under quadratic (squared error) loss, the Bayesian estimate of a parameter θ is:

The Bayesian estimate under squared error loss is the posterior mean. Minimising the posterior expected value of (θ - a) squared gives a equal to E[θ | x]. The median corresponds to absolute error loss and the mode to zero-one loss.

  1. Athe posterior mode
  2. Bthe posterior meanCorrect
  3. Cthe posterior median
  4. Dthe prior mean
  5. the maximum likelihood estimate

Explanation

Minimising the expected squared error E[(θ - a)^2 | x] gives a = E[θ | x], the posterior mean. The posterior median minimises expected absolute error loss, and the mode corresponds to all-or-nothing (0-1) loss.

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