Posterior Expected Loss

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A Posterior Expected Loss is an Expected Value or a Loss Function that is based on a posterior distribution.



References

2019

2011

  • (Wikipedia, 2019) ⇒ http://en.wikipedia.org/wiki/Loss_function#Bayesian_expected_loss
    • In a Bayesian approach, the expectation is calculated using the posterior distribution π* of the parameter θ: [math]\displaystyle{ \rho(\pi^*,a) = \int_\Theta L(\theta, a) \, \operatorname{d} \pi^* (\theta) }[/math]. One then should choose the action a* which minimises the expected loss. Although this will result in choosing the same action as would be chosen using the Bayes risk, the emphasis of the Bayesian approach is that one is only interested in choosing the optimal action under the actual observed data, whereas choosing the actual Bayes optimal decision rule, which is a function of all possible observations, is a much more difficult problem.