Bayes Theorem

Source: https://arbital.com/p/bayes_rule/

If H_i and H_j are hypotheses and e is a piece of evidence, Bayes’ rule states:

Waterfalls are one way of visualizing the “odds form” of “Bayes’ rule”, which states that the prior odds times the likelihood ratio equals the posterior odds. In turn, this rule can be seen as formalizing the notion of “the strength of evidence” or “how much a piece of evidence should make us update our beliefs”.

More generally, suppose we have a medical test that detects a sickness with a 90% true positive rate (10% false negatives) and a 30% false positive rate (70% true negatives). A positive result on this test represents the same strength of evidence as a test with 60% true positives and 20% false positives. A negative result on this test represents the same strength of evidence as a test with 9% false negatives and 63% true negatives.

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uid: 202212092211 tags: #insights

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