Editing Loss function (section)

==Decision rules==
A [[decision rule]] makes a choice using an optimality criterion. Some commonly used criteria are:

*'''[[Minimax]]''': Choose the decision rule with the lowest worst loss — that is, minimize the worst-case (maximum possible) loss: <math display="block"> \underset{\delta} {\operatorname{arg\,min}} \ \max_{\theta \in \Theta} \ R(\theta,\delta). </math>
*'''[[Invariant estimator|Invariance]]''': Choose the decision rule which satisfies an invariance requirement.
*Choose the decision rule with the lowest average loss (i.e. minimize the [[expected value]] of the loss function): <math display="block"> \underset{\delta} {\operatorname{arg\,min}} \operatorname{E}_{\theta \in \Theta} [R(\theta,\delta)] = \underset{\delta} {\operatorname{arg\,min}} \ \int_{\theta \in \Theta} R(\theta,\delta) \, p(\theta) \,d\theta. </math>