WEBVTT

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What we really said that we had a situation that prior

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a test is a certain sensitivity and a certain specificity.

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When you receive say a positive test result, what you do is you take your prior,

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you multiply in the probability of this test result.

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Given C, and you multiply in the probability of the test result given not C.

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So this is your branch for the consideration that you have cancer.

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This is your branch for the consideration you have no cancer.

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When you're done with this, you arrive at a number that now combines the cancer

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hypothesis with the test result.

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Both for the cancer hypothesis and the not cancer hypothesis.

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Now what you do, you add those up.

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And they normally don't add up to one.

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You get a certain quantity,

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which happens to be the total probability that the test is what it was.

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This case positive.

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And all you do next is divide or

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normalize this thing over here by the sum over here.

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And the same on the right side.

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The divider is the same for

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both cases because this is your cancer range, your non cancer range.

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But this guy doesn't rely on the cancer variable anymore.

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What you now get out is the desired posterior probability, and

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those add up to one if you did everything correct as shown over here.

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This is your algorithm for Bayes Rule