 Suppose that being over 7 feet tall indicates with 60% probability that someone is a basketball player, and carrying a basketball indicates this with 72% probability. If you see someone who is over 7 feet tall and carrying a basketball, what is the probability that they're a basketball player? If a and b are the probabilities associated with two independent pieces of evidence, then combined they indicate a probability of:
ab
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ab + (1 - a)(1 - b)
So in this case our answer is:
(.60)(.72)
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(.60)(.72) + (1 - .60)(1 - .72)
which is .794. There is a 79.4% chance that the person is a basketball player.When there are more than two pieces of evidence, the formula expands as you might expect:
abc
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abc + (1 - a)(1 - b)(1 - c)
In the case of spam filtering, what we want to calculate is the probability
that the mail is a spam, and the individual pieces of evidence
a, b, c, ... are the
spam probabilities associated with each of the words in the mail.For a good explanation of the background, see: http://www.mathpages.com/home/kmath267.htm. |