Editing 2059: Modified Bayes' Theorem
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==Explanation== | ==Explanation== | ||
β | {{w|Bayes' Theorem}} is an equation in | + | {{incomplete|Please check the language, mention any other reason here, or remove this tag.}} |
+ | The {{w|Bayes' Theorem}} is an equation in statistics that gives the probability of a given hypothesis accounting not only for a single experiment or observation but also for your existing knowledge about the hypothesis, i.e. its prior probability. Randall's modified form of the equation also purports to account for the probability that you are indeed applying Bayes' Theorem itself correctly by including that as a term in the equation. | ||
Bayes' theorem is: | Bayes' theorem is: | ||
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It is a {{w|Linear interpolation|linear-interpolated}} weighted average of the belief from before the calculation and the belief after applying the theorem correctly. This goes smoothly from not believing the calculation at all up to be fully convinced to it. | It is a {{w|Linear interpolation|linear-interpolated}} weighted average of the belief from before the calculation and the belief after applying the theorem correctly. This goes smoothly from not believing the calculation at all up to be fully convinced to it. | ||
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The title text suggests that an additional term should be added for the probability that the Modified Bayes Theorem is correct. But that's ''this'' equation, so it would make the formula self-referential, unless we call the result the Modified Modified Bayes Theorem. It could also result in an infinite regress -- needing another term for the probability that the version with the probability added is correct, and another term for that version, and so on. If the modifications have a limit, then a Modified<sup>ω</sup> Bayes Theorem would be the result, but then another term for whether it's correct is needed, leading to the Modified<sup>ω+1</sup> Bayes Theorem, and so on through every {{w|ordinal number}}. | The title text suggests that an additional term should be added for the probability that the Modified Bayes Theorem is correct. But that's ''this'' equation, so it would make the formula self-referential, unless we call the result the Modified Modified Bayes Theorem. It could also result in an infinite regress -- needing another term for the probability that the version with the probability added is correct, and another term for that version, and so on. If the modifications have a limit, then a Modified<sup>ω</sup> Bayes Theorem would be the result, but then another term for whether it's correct is needed, leading to the Modified<sup>ω+1</sup> Bayes Theorem, and so on through every {{w|ordinal number}}. |