The coin flipping example used in the article is pretty weak. We are convinced that the coin is unfair when we see "HHHHHHHH" but not "HHTHTHTHH" because the fo

The coin flipping example used in the article is pretty weak. We are convinced that the coin is unfair when we see "HHHHHHHH" but not "HHTHTHTHH" because the former event is more likely given an unfair coin. We choose the hypothesis that makes the data most likely. I doubt the author's of the undergraduate textbook were unaware of maximum likelihood estimation. I suspect that the post's author simply did not read far enough into his textbook and got hung up on a simplified model given in an early chapter. Any hypothesis we test about the coin's "fairness" is implicitly a test of how close p is to 1/2. The only difference between a frequentist analysis and a bayesian analysis in this case would be that the latter might impose a prior on p (although in reality we would likely impose a uniform prior, rendering the two analyses identical).