On Thomas Bayes’ Theorem

Courtesy: www.CertifiedMedicalPlanner.org

The Theory of Conditional Probability

In probability theory and statistics, Bayes’ theorem (alternatively Thomas Bayes’ law or Bayes’ rule, also written as Bayes’s theorem) describes the probability of an event, based on prior knowledge of conditions that might be related to the event.

Examples:

For example, if cancer is related to age, then, using Bayes’ theorem, a person’s age can be used to more accurately assess the probability that they have cancer, compared to the assessment of the probability of cancer made without knowledge of the person’s age.

As another example, imagine there is a drug test that is 98% accurate, meaning 98% of the time it shows a true positive result for someone using the drug and 98% of the time it shows a true negative result for nonusers of the drug. Next, assume 0.5% of people use the drug. If a person selected at random tests positive for the drug, the following calculation can be made to see whether the probability the person is actually a user of the drug.

(0.98 x 0.005) / [(0.98 x 0.005) + ((1 – 0.98) x (1 – 0.005))] = 0.0049 / (0.0049 + 0.0199) = 19.76%

Bayes’ theorem shows that even if a person tested positive in this scenario, it is actually much more likely the person is not a user of the drug.

 Assessment

In finance, Bayes’ theorem can be used to rate the risk of lending money to potential borrowers.

MORE: https://www.coursera.org/lecture/combinatorics/bayes-theorem-sqAyt

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