Do you take into account the possibility that you miscounted, or are hallucinating, or any of the other events that are far more likely explanations than that it comes up heads with probability 49% and it came up heads that often just by chance?
This comment rubbed me the wrong way and I couldn't figure out why at first, which is why I went for a pithy response.
I think what's going on is I was reacting to the pragmatics of your exchange with Coscott. Coscott informally specified a model and then asked what we could conclude about a parameter of interest, which coin was chosen, given a sufficient statistic of all the coin toss data, the number of heads observed.
This is implicitly a statement that model checking isn't important in solving the problem, because everything that could be used for model ...
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
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