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A comment on Why is everything based on likelihoods even though likelihoods are so small?. Parent comment
The number of heads is a sufficient statistic, so we'll get the same likelihood ratios out, but the likelihood values themselves will be larger.
You could make a similar point about the original CrossValidated Normal(0, 1)^N example by summarizing the data with the mean and sum of squares.
This doesn't work if the data were Cauchy(0, 1)^N instead.
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The number of heads is a sufficient statistic, so we'll get the same likelihood ratios out, but the likelihood values themselves will be larger.
You could make a similar point about the original CrossValidated Normal(0, 1)^N example by summarizing the data with the mean and sum of squares.
This doesn't work if the data were Cauchy(0, 1)^N instead.