0:00:00.350,0:00:04.820
What we really said that we had a situation that prior
0:00:04.820,0:00:09.970
a test is a certain sensitivity and a certain specificity.
0:00:09.970,0:00:15.120
When you receive say a positive test result, what you do is you take your prior,
0:00:15.120,0:00:18.640
you multiply in the probability of this test result.
0:00:18.640,0:00:24.240
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.
0:00:28.470,0:00:31.740
This is your branch for the consideration you have no cancer.
0:00:31.740,0:00:35.610
When you're done with this, you arrive at a number that now combines the cancer
0:00:35.610,0:00:37.580
hypothesis with the test result.
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Both for the cancer hypothesis and the not cancer hypothesis.
0:00:42.950,0:00:45.680
Now what you do, you add those up.
0:00:45.680,0:00:49.580
And they normally don't add up to one.
0:00:49.580,0:00:51.080
You get a certain quantity,
0:00:51.080,0:00:55.240
which happens to be the total probability that the test is what it was.
0:00:55.240,0:00:56.580
This case positive.
0:00:56.580,0:00:59.185
And all you do next is divide or
0:00:59.185,0:01:04.160
normalize this thing over here by the sum over here.
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And the same on the right side.
0:01:06.260,0:01:08.030
The divider is the same for
0:01:08.030,0:01:12.990
both cases because this is your cancer range, your non cancer range.
0:01:12.990,0:01:15.325
But this guy doesn't rely on the cancer variable anymore.
0:01:15.325,0:01:19.950
What you now get out is the desired posterior probability, and
0:01:19.950,0:01:23.720
those add up to one if you did everything correct as shown over here.
0:01:23.720,0:01:25.510
This is your algorithm for Bayes Rule