Re: [math-fun] optimal advance tournament scheduling
Just in case anyone else on math-fun actually knows what maximum likelihood means ... ... it makes no sense whatoever to talk about maximum likelihood unless (as has no been done below) this is in the context of a PARAMETRIZED FAMILY OF DISTRIBUTIONS. Then you say under which one, as the probability model, makes what happened more likely than the others. So saying what maximum likelihood will or will not predict WITHOUT reference to a model is utterly meaningless. —Dan ---- Perhaps this is interesting: if we have three players who have played three
games and created a cycle (A beat B, B beat C, C beat A), a three-way tie in strength is NOT the maximum-likelihood solution;
I think in the case I described we do have a parametrized family of distributions; the parameters are Prob(A beats B) et cetera, and that induces a probability distribution on tournament outcomes. Am I missing something? On Thu, Jun 27, 2019 at 6:30 PM Dan Asimov <dasimov@earthlink.net> wrote:
Just in case anyone else on math-fun actually knows what maximum likelihood means ...
... it makes no sense whatoever to talk about maximum likelihood unless (as has no been done below) this is in the context of a PARAMETRIZED FAMILY OF DISTRIBUTIONS. Then you say under which one, as the probability model, makes what happened more likely than the others.
So saying what maximum likelihood will or will not predict WITHOUT reference to a model is utterly meaningless.
—Dan
---- Perhaps this is interesting: if we have three players who have played three
games and created a cycle (A beat B, B beat C, C beat A), a three-way tie in strength is NOT the maximum-likelihood solution;
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Dan Asimov -
Michael Collins