Comments on: Visualizing Bayes’ theorem

By: Mark

Mark — Sun, 22 Jan 2012 15:14:38 +0000

Outstanding! I’ve been trying to get my head around this for some time and your explanation made everything fall into place. Nicely done. Thanks for posting this.

By: Hemant Patel

Hemant Patel — Thu, 08 Dec 2011 21:27:52 +0000

Very usefull article

Wiki page must have link of Such a good and easy to under stand article.

Thank you.

By: freethoughtful

freethoughtful — Sat, 26 Nov 2011 05:41:32 +0000

Nicely done. A similar (and equally intuitive and effective) visual explanation of conditional probability and Bayes theorem based on Venn diagrams can be found in Bolstad’s textbook on Bayesian Statistics.

By: E. Fitzgerald

E. Fitzgerald — Mon, 14 Nov 2011 23:33:48 +0000

Dear Oscar,

A clear presentation – a pleasure to read…

By: Ann

Ann — Tue, 01 Nov 2011 07:24:31 +0000

very useful. thank you

By: ob

ob — Thu, 27 Oct 2011 18:46:54 +0000

I didn’t want to overcomplicate the example.

By: ob

ob — Thu, 27 Oct 2011 18:46:24 +0000

80% of women with breast cancer will get a positive mammogram means that P(positive mammogram | woman has cancer) = 0.8.
The remaining 20% is the probability of getting a negative mammogram given that the woman has cancer.

The 9.6 comes from the other part of the population, i.e. women without cancer that also get a positive mammogram.

In general, P(B | A) + P(¬B | A) will sum to 1, but P(B|A) + P(B|¬A) will not as they are unrelated probabilities.

By: ob

ob — Thu, 27 Oct 2011 18:42:41 +0000

P(B) is the total probability of B, it’s the chance of B happening regardless of whether A happens. Thus, P(B) = P(B|A)P(A) + P(B|¬A)P(¬A).

By: Mary

Mary — Sat, 22 Oct 2011 18:57:01 +0000

I agree, I can’t understand how to figure out Pr (B) :(

I’ve got a stats module in my masters and having come from a non mathematical background… I’m struggling a bit.

By: Ganesh Krishnan

Ganesh Krishnan — Sat, 22 Oct 2011 03:46:53 +0000

>80% of women with breast cancer will get positive mammograms. 9.6% of women
>without breast cancer will also get positive mammograms.

80% have cancer and 9.6% don’t have cancer (when you have positive mammogram). Why doesn’t 80 + 9.6 addup to 100%? What probabilities are remaining?

Damn! I wish I had slept in my math classes

By: luis

luis — Thu, 20 Oct 2011 18:43:09 +0000

I think your explanation is flawed. You said P(A) = | A | / |U|, but that is only true if all elements of A have the same probability. In general that is a false statement.

By: Visualizing Bayes’s theorem | The Personal Blog of Artem Koval, M.Sc.

Visualizing Bayes’s theorem | The Personal Blog of Artem Koval, M.Sc. — Thu, 20 Oct 2011 17:45:27 +0000

[...] an incredible article! I wish I had this explanation in the high school. As a fully qualified mathematician I want to say [...]

By: Jeffrey Horn

Jeffrey Horn — Fri, 23 Sep 2011 05:38:28 +0000

I should have said this was the natural error of ignoring base rates, not inverting probabilities.

By: Jeffrey Horn

Jeffrey Horn — Fri, 23 Sep 2011 05:31:42 +0000

I drew up a similar explanation about a year ago to explain why, even though there are more poor whites than poor blacks in the world, the perception that most black people are poor is not incorrect. I used current census data at the time, and realized the person registering the complaint on twitter was making the very natural error of inverting probabilities. Here was my illustration: http://cl.ly/V2Y

By: Perpetual BETA: this sites 2010 to-do list | Fellow Creative

Perpetual BETA: this sites 2010 to-do list | Fellow Creative — Mon, 19 Sep 2011 09:38:57 +0000

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