Editing 1132: Frequentists vs. Bayesians
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==Explanation== | ==Explanation== | ||
+ | {{incomplete|The section "Mathematical and scientific details" isn't real science. A title "Mathematical and scientific nonsense" would be more accurate, nonetheless something else like science should be better. Fictional? or Hypothetical?}} | ||
This comic is a joke about jumping to conclusions based on a simplistic understanding of probability. The "{{w|base rate fallacy}}" is a mistake where an unlikely explanation is dismissed, even though the alternative is even less likely. In the comic, a device tests for the (highly unlikely) event that the sun has exploded. A degree of random error is introduced, by rolling two {{w|dice}} and lying if the result is double sixes. Double sixes are unlikely (1 in 36, or about 3% likely), so the statistician on the left dismisses it. The statistician on the right has (we assume) correctly reasoned that the sun exploding is ''far more'' unlikely, and so is willing to stake money on his interpretation. | This comic is a joke about jumping to conclusions based on a simplistic understanding of probability. The "{{w|base rate fallacy}}" is a mistake where an unlikely explanation is dismissed, even though the alternative is even less likely. In the comic, a device tests for the (highly unlikely) event that the sun has exploded. A degree of random error is introduced, by rolling two {{w|dice}} and lying if the result is double sixes. Double sixes are unlikely (1 in 36, or about 3% likely), so the statistician on the left dismisses it. The statistician on the right has (we assume) correctly reasoned that the sun exploding is ''far more'' unlikely, and so is willing to stake money on his interpretation. | ||
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The title text refers to a classic series of logic puzzles known as {{w|Knights and Knaves#Fork in the road|Knights and Knaves}}, where there are two guards in front of two exit doors, one of which is real and the other leads to death. One guard is a liar and the other tells the truth. The visitor doesn't know which is which, and is allowed to ask one question to one guard. The solution is to ask either guard what the other one would say is the real exit, then choose the opposite. Two such guards were featured in the 1986 Jim Henson movie ''{{w|Labyrinth (1986 film)|Labyrinth}}'', hence the mention of "A LABYRINTH GUARD" here. A labyrinth was also mentioned in [[246: Labyrinth Puzzle]]. | The title text refers to a classic series of logic puzzles known as {{w|Knights and Knaves#Fork in the road|Knights and Knaves}}, where there are two guards in front of two exit doors, one of which is real and the other leads to death. One guard is a liar and the other tells the truth. The visitor doesn't know which is which, and is allowed to ask one question to one guard. The solution is to ask either guard what the other one would say is the real exit, then choose the opposite. Two such guards were featured in the 1986 Jim Henson movie ''{{w|Labyrinth (1986 film)|Labyrinth}}'', hence the mention of "A LABYRINTH GUARD" here. A labyrinth was also mentioned in [[246: Labyrinth Puzzle]]. | ||
− | ===Further | + | ===Further mathematical exploration=== |
As mentioned, this is an instance of the {{w|base rate fallacy}}. If we treat the "truth or lie" setup as simply modelling an inaccurate test, then it is also specifically an illustration of the {{w|false positive paradox}}: A test that is rarely wrong, but which tests for an event that is even rarer, will be more often wrong than right when it says that the event has occurred. | As mentioned, this is an instance of the {{w|base rate fallacy}}. If we treat the "truth or lie" setup as simply modelling an inaccurate test, then it is also specifically an illustration of the {{w|false positive paradox}}: A test that is rarely wrong, but which tests for an event that is even rarer, will be more often wrong than right when it says that the event has occurred. | ||