Bayes - LearningObjectives...

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Learning Objectives State “total probability” relationship and use to calculate  probabilities State Bayes’ theorem and use to calculate probabilities Define and calculate the following quantities, using  Bayes’ theorem if needed: Positive predictive value Sensitivity Specificity Prevalence
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Example Suppose that a test for cancer is 99% sensitive and  85% specific and that the prevalence of cancer in  the test population is 3%.  What is the positive  predictive value of the test?
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Total Probability Rule The total unconditional probability of an event B  can be written as a weighted average of the  conditional probabilities of a set of disjoint events  A 1 , A 2 …A n , as long as A 1 , A 2 …A n  form a  partition of the sample space P ( B ) = P ( A 1 Ç B ) +L P ( A n Ç B ) P ( B ) = P ( B | A 1 ) P ( A 1 ) +L + P ( B | A n ) P ( A n )
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Bayes - LearningObjectives...

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