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  "body": "\n## Summary\n\nThe risk function of a decision rule gives, for each value of the unknown parameter, the expected [[loss|3BTG6VVCGZ]] of the rule.\nThe data are drawn from the model with that parameter.\nIt turns a random loss into a deterministic function of the parameter.\nDecision rules are compared through their risk functions, which leads to the notions of admissible, minimax and Bayes rules.\n\n## Explanations\n\n### L1 human\n\nA rule that turns data into a decision is sometimes lucky and sometimes unlucky.\nThe risk is its average loss over many repetitions of the experiment, for a fixed true parameter.\nBecause the true parameter is unknown, one looks at the whole curve $\\theta \\mapsto R(\\theta, \\delta)$.\nFor example, estimating a normal mean $\\theta$ by the mean of $n$ observations with variance $1$ has risk $1/n$ under squared error, the same for every $\\theta$.\n",
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