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?
When I know I’m to be visited by one of my parents and I see someone who looks like my mother, should my first thought be “that person looks so unlike my father that maybe it is him and I’m having a stroke”? Should I damage my eyes to the point where this phenomenon doesn’t occur to spare myself the confusion?
If you’re being asked to estimate the probability that you’re being visited by your father then yes you probably should be considering the possibility that you are seeing him but you’re having a stroke.
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.
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?
When I know I’m to be visited by one of my parents and I see someone who looks like my mother, should my first thought be “that person looks so unlike my father that maybe it is him and I’m having a stroke”? Should I damage my eyes to the point where this phenomenon doesn’t occur to spare myself the confusion?
If you’re being asked to estimate the probability that you’re being visited by your father then yes you probably should be considering the possibility that you are seeing him but you’re having a stroke.
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.