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  • $\begingroup$ They are totally different things, so could you clarify what makes you consider them "essentially the same"? $\endgroup$ Commented May 24, 2016 at 19:21
  • $\begingroup$ Sorry I have edited my question. I hope my question is clearer now. $\endgroup$ Commented May 25, 2016 at 1:37
  • $\begingroup$ What you describe seems to be a Bayes classifier, not a Bayes optimal classifier. $\endgroup$ Commented Feb 17, 2019 at 10:47