This link has been bookmarked by 71 people . It was first bookmarked on 01 May 2009, by someone privately.
-
19 Aug 13
-
25 Mar 11
Lily ChangP(A|B)= P(B|A)*P(A) / P(B) P(A|B) 的意思是：in a given population of B, the probability of having A. likewise, P(B|A): in a given population of A, the probability of having B.
-
compute the probability of both events occurring (AB is a shorthand for A∩B) in the same way.
-
the question we'd like answered is "given that the test is positive for a randomly selected individual, what is the probability that said individual has cancer?". In terms of our Venn diagram, that translates to "given that we are in region B, what is the probability that we are in region AB?" or stated another way "if we make region B our new Universe, what is the probability of A?". The notation for this is P(A|B) and it is read "the probability of A given B".
-
So what is it? Well, it should be
And if we divide both the numerator and the denominator by |U|
we can rewrite it using the previously derived equations as -
What we've effectively done is change the Universe from U (all people), to B (people for whom the test is positive), but we are still dealing with probabilities defined in U. -
Now let's ask the converse question "given that a randomly selected individual has cancer (event A), what is the probability that the test is positive for that individual (event AB)?". It's easy to see that it is
Now we have everything we need to derive Bayes' theorem, putting those two equations together we get
which is to say P(AB) is the same whether you're looking at it from the point of view of A or B, and finally
-
9.6% of women without breast cancer will also get positive mammograms.
-
cover 80% of the area of event A
-
9.6% of the area outside of event A.
-
It is clear from the diagram that if we restrict our universe to B (women with positive mammograms), only a small percentage actually have cancer. According to the article, most doctors guessed that the answer to the question was around 80%, which is clearly impossible looking at the diagram!
-
Bayes' theorem
-
-
23 Feb 11
-
26 Mar 10
-
23 Sep 09
-
13 Aug 09
-
31 Jul 09
-
30 Jul 09
scmoralOne of the easiest ways to understand probabilities is to think of them in terms of Venn Diagrams. You basically have a Universe with all the possible outcomes (of an experiment for instance), and you are interested in some subset of them, namely some eve
statistics bayesian classification datamining ir textmining textanalysis linguistics bayes math mathematics algorithms categorization
-
01 Jun 09
icytopReally really good explanation of Bayes' theorem. Bravo!
-
19 May 09
-
11 May 09
Michael C. HarrisOne of the easiest ways to understand probabilities is to think of them in terms of Venn Diagrams.
-
10 May 09
-
08 May 09
-
05 May 09
-
04 May 09
-
nealrichterRT @the_real_r2d2 Visualizing Bayes’ theorem http://tinyurl.com/ck32s6 [from http://twitter.com/nealrichter/statuses/1697593178]
tweecious Cancer Health Breastcancer Breast Mammography ConditionsandDiseases Screening SupportGroups
-
Gregory LouieVisualizing Bayes’ theorem
I recently came up with what I think is an intuitive way to explain Bayes’ Theorem. I searched in google for a while and could not find any article that explains it in this particular way.
Of course there’s the wikipedia page, that long article by Yudkowsky, and a bunch of other explanations and tutorials. But none of them have any pictures. So without further ado, and with all the chutzpah I can gather, here goes my explanation. -
03 May 09
-
Sarawut SukjaiI recently came up with what I think is an intuitive way to explain Bayes' Theorem. I searched in google for a while and could not find any article that
-
02 May 09
-
Kansiree Sang-EkI recently came up with what I think is an intuitive way to explain Bayes' Theorem. I searched in google for a while and could not find any article that
-
ken .With simple venn diagrams, visual overlaps rather than abstract chicken scratches
communication education learning simplicity statistics visualization
-
01 May 09
-
Would you like to comment?
Join Diigo for a free account, or sign in if you are already a member.