The Coin Toss
Three heads, two philosophies. The bartender flips three heads in a row. Professor Fisher wants a larger sample; Dr. Bayes updates his belief only slightly.
Behind the joke.
A fair coin lands heads three times in a row one time in eight, so the streak is weak evidence of bias. Fisher withholds judgment until a larger sample arrives. Dr. Bayes starts from a strong prior that most coins are fair and moves only a little. With so little data, both approaches reach much the same practical conclusion, which Fisher finds annoying.
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Bartender: Heads three times in a row. Biased coin?
Professor Fisher: Three flips prove nothing. I need a much larger sample.
Dr. Bayes: My prior is that most coins are fair. Three heads nudges me a little, not a lot.
Bartender: So he waits for more data, and you update gradually?
Dr. Bayes: Exactly.
Professor Fisher: Annoyingly, yes.