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 checking, e.g., statistics on runs to verify independence, the number of tails observed to check against a type of miscounting where the number of tosses don’t add to 1,000,000, mental status inventories to detect hallucination, etc., is left out of the statistic communicated.
Maybe Coscott (the fictional version who flipped all those coins) did model checking or maybe not, but if it was done and the data suggested miscounting or hallucination, then Coscott wouldn’t have stated the problem like this.
So, yeah, the points you raise are valid object-level ones, but bringing them up this way in a problem poser / problem solver context was really unexpected and seemed to violate the norms for this sort of exchange.
I suppose my point was that assuming normal distribution can give you far more extreme probabilities than could ever realistically be justified. It would probably be better if I just said it like that.
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 checking, e.g., statistics on runs to verify independence, the number of tails observed to check against a type of miscounting where the number of tosses don’t add to 1,000,000, mental status inventories to detect hallucination, etc., is left out of the statistic communicated.
Maybe Coscott (the fictional version who flipped all those coins) did model checking or maybe not, but if it was done and the data suggested miscounting or hallucination, then Coscott wouldn’t have stated the problem like this.
So, yeah, the points you raise are valid object-level ones, but bringing them up this way in a problem poser / problem solver context was really unexpected and seemed to violate the norms for this sort of exchange.
I suppose my point was that assuming normal distribution can give you far more extreme probabilities than could ever realistically be justified. It would probably be better if I just said it like that.