Editing 1132: Frequentists vs. Bayesians
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Since the likelihood of rolling double sixes is below this 5% threshold, the "frequentist" decides (by this rule of thumb) to accept the detector's output as correct. The "{{w|Bayesian statistics|Bayesian}}" statistician has, instead, applied at least a small measure of probabilistic reasoning ({{w|Bayesian inference}}) to determine that the unlikeliness of the detector lying is greatly outweighed by the unlikeliness of the sun exploding. Therefore, he concludes that the sun has ''not'' exploded and the detector is lying. | Since the likelihood of rolling double sixes is below this 5% threshold, the "frequentist" decides (by this rule of thumb) to accept the detector's output as correct. The "{{w|Bayesian statistics|Bayesian}}" statistician has, instead, applied at least a small measure of probabilistic reasoning ({{w|Bayesian inference}}) to determine that the unlikeliness of the detector lying is greatly outweighed by the unlikeliness of the sun exploding. Therefore, he concludes that the sun has ''not'' exploded and the detector is lying. | ||
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The line, "Bet you $50 it hasn't", is a reference to the approach of a leading Bayesian scholar, {{w|Bruno de Finetti}}, who made extensive use of bets in his examples and thought experiments. See {{w|Coherence (philosophical gambling strategy)}} for more information on his work. In this case, however, the bet is also a joke because we would all be dead if the sun exploded. If the Bayesian wins the bet, he gets money, and if he loses, they'll both be dead before money can be paid. This underlines the absurdity of the premise and emphasizes the need to consider context when examining probability. | The line, "Bet you $50 it hasn't", is a reference to the approach of a leading Bayesian scholar, {{w|Bruno de Finetti}}, who made extensive use of bets in his examples and thought experiments. See {{w|Coherence (philosophical gambling strategy)}} for more information on his work. In this case, however, the bet is also a joke because we would all be dead if the sun exploded. If the Bayesian wins the bet, he gets money, and if he loses, they'll both be dead before money can be paid. This underlines the absurdity of the premise and emphasizes the need to consider context when examining probability. |