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

Under squared error loss, the Bayes estimate of a parameter θ is which feature of the posterior distribution?

Under squared error loss the Bayes estimate is the posterior mean. Setting the derivative of the expected loss to zero gives a = E[θ|x]. The median corresponds to absolute error loss, and the mode to all-or-nothing loss.

  1. AThe posterior mode
  2. BThe posterior meanCorrect
  3. CThe posterior median
  4. DThe posterior variance
  5. The prior mean

Explanation

Minimising expected squared error loss E[(θ−a)²|x] over a gives a = E[θ|x], the posterior mean. The median is optimal for absolute error loss and the mode for all-or-nothing loss.

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