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  "body": "\n## Summary\n\nStatistical decision theory treats statistical problems as decisions under uncertainty.\nA statistician observes data from a model with an unknown parameter and chooses an action by a decision rule.\nThe statistician then pays a [[loss|3BTG6VVCGZ]] that depends on the action and the true parameter.\nRules are compared through their [[risk functions|N26TSVRH2S]], which gives a common frame for estimation, testing and prediction.\n\n## Explanations\n\n### L1 human\n\nEstimating a number, testing a hypothesis or predicting a value are all ways of making a decision from data.\nDecision theory asks the user to say how costly each kind of mistake is, and then looks for the rule with the smallest average cost.\nUsually no rule is best for every possible truth at once, so one needs a criterion.\nCommon criteria are to protect against the worst case (minimax), to average over a prior (Bayes), or at least to discard rules that are beaten everywhere (admissibility).\n",
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