Bayes’ Theorem is written here using H (for hypothesis) and e (for evidence). So in this little scenario, the hypothesis is ‘having a cold’ and the evidence is ‘having a runny nose’. Then Bayes’ theorem looks like this: And in plain English, you would read it like this: “The probability that the hypothesis is true, given the evidence, is equal to the likelihood of the evidence occurring when the hypothesis is true, times the probability of the hypothesis being true before seeing any evidence, divided by the probability of the evidence occurring under all possible hypotheses.”

Or in the cold scenario: “The probability that I have a cold (given that I have a runny nose) is equal to the probability of having a runny nose when I have a cold, times the probability of having a cold (regardless of whether I have a runny nose or not), divided by the probability of having a runny nose (regardless of whether it’s caused by a cold or something else).”

Summary:

P(H|E) = the probability that I have a cold, given that I have a runny nose

P(E|H) = the probability of having a runny nose when I have a cold

P(H) = the probability of having a cold, without knowing what my symptoms are

P(E) = the probability of having a runny nose, whatever the cause may be

via Bayes’ Rule and Bomb Threats » Psychology In Action.

http://betterexplained.com/articles/an-intuitive-and-short-explanation-of-bayes-theorem/

# Bayes is back on xkcd

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