Friday, February 26, 2010

About Bayes and data mining

Wiki says
In probability theory, Bayes' theorem, often called Bayes' law or Bayes' rule, and named after Rev. Thomas Bayes (pronounced /bejz/), shows how one conditional probability (such as the probability of a hypothesis given observed evidence) depends on its inverse (in this case, the probability of that evidence given the hypothesis).

The key idea is that the probability of event A (e.g., having breast cancer) given event B (having a positive mammogram) depends not only on the relationship between A and B (i.e., the accuracy of mammograms) but on the absolute probability of A independent of B (i.e., the incidence of breast cancer in general). For example, even if mammograms are 95% accurate, a positive mammogram is still most likely to be a false positive, given the relative rarity of breast cancer (about 1 in a 1000).

This result violates most people's intuition.

Curios and mysterious math even for today's times :)

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