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Bayes´ Theorem

Bayes´ Theorem:

Bayes theorem is a formula for revising a priori probabilities after receiving new information. The revised probabilities are called posterior probabilities. For example, consider the probability that you will develop a specific cancer in the next year. An estimate of this probability based on general population data would be a prior estimate; a revised (posterior) estimate would be based on both on the population data and the results of a specific test for cancer.

The formula for Bayes Theorem is as follows:

The best way to understand the terms is to look at an example. Consider a screening test for intestinal tumors. Let Ai = A1 = the event "tumor present", "B" the event "screening test positive" and "A2" the event "tumor not present" with no further A´s.

If you have a tumor, the screening test has an 85% chance of catching it -- P(B|A1) = .85. However, it also has a 10% chance of falsely indicating "tumor present" when there is no tumor P(B|A2) = .10. The probability of a person having a tumor is .02 P(A1) = .02.

If the screening test is positive, what is the probability that you have a tumor?

.02*.85/(.02*.85+.98*.10)

= .017/(.017+ .098)

= .148

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Courses Using This Term

Biostatistics 1 – For Medical Science and Public Health
This course will teach you the principal statistical concepts used in medical and health sciences. Basic concepts common to all statistical analysis are reviewed, and those concepts with specific importance in medicine and health are covered in detail.
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