jsalvatier comments on The Optimizer's Curse and How to Beat It - Less Wrong
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In statistics the solution you describe is called Hierarchical or Multilevel Modeling. You assume that you data is drawn from a set of distributions which have their parameters drawn from another distribution. This automatically shrinks your estimates of the distributions towards the mean. I think it's a pretty useful trick to know and I think it would be good to do a writeup but I think you might need to have a decent grasp of bayesian statistics first.