by lifeis42 on Thu Dec 11, 2008 1:52 am
i dont much understand bayes but i seem to recall hereing it once on the tv show numbers
Now i kind get it this a realy good example
Example 1: Drug testing
Bayes' theorem is useful in evaluating the result of drug tests. Suppose a certain drug test is 99% sensitive and 99% specific, that is, the test will correctly identify a drug user as testing positive 99% of the time, and will correctly identify a non-user as testing negative 99% of the time. This would seem to be a relatively accurate test, but Bayes' theorem will reveal a potential flaw. Let's assume a corporation decides to test its employees for opium use, and 0.5% of the employees use the drug. We want to know the probability that, given a positive drug test, an employee is actually a drug user. Let "D" be the event of being a drug user and "N" indicate being a non-user. Let "+" be the event of a positive drug test. We need to know the following:
P(D), or the probability that the employee is a drug user, regardless of any other information. This is 0.005, since 0.5% of the employees are drug users. This is the prior probability of D.
P(N), or the probability that the employee is not a drug user. This is 1 âˆ’ P(D), or 0.995.
P(+|D), or the probability that the test is positive, given that the employee is a drug user. This is 0.99, since the test is 99% accurate.
P(+|N), or the probability that the test is positive, given that the employee is not a drug user. This is 0.01, since the test will produce a false positive for 1% of non-users.
P(+), or the probability of a positive test event, regardless of other information. This is 0.0149 or 1.49%, which is found by adding the probability that a true positive result will appear (= 99% x 0.5% = 0.495%) plus the probability that a false positive will appear (= 1% x 99.5% = 0.995%). This is the prior probability of +.
Given this information, we can compute the posterior probability P(D|+) of an employee who tested positive actually being a drug user:
Despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%, so it is actually more likely that the employee is not a drug user. The rarer the condition for which we are testing, the greater the percentage of positive tests that will be false positives.
It can also applie to the monty hall problem the three diffrent colored door one and theres a prize behind one and the host opens one of the ones you don,t chose then gives you the option to pick agian
trancendentalism thats the way to go