Comments on: Visualizing Bayes’ theorem

By: Chris

Chris — Tue, 08 May 2012 11:40:00 +0000

Thanks! You proved how truly understanding something means being able to teach it in a way that grade school kids can understand :)

By: Masud

Masud — Mon, 16 Apr 2012 12:10:07 +0000

Thanks for the explanation

By: Sree

Sree — Sun, 18 Mar 2012 09:01:24 +0000

Thanx Oscar , that was really intuitive ..

By: BCPower

BCPower — Thu, 09 Feb 2012 12:49:53 +0000

Furthermore, the simplified formula that I mentioned above could, consequently be compounded by the number of given circumstances. Assuming no variables are defines as the graphic at the top suggests, it could be said that the Bayes formula would compound in similar, possible equations much like possible combinations of a lock. That is to say, if given a combination lock with 4 dials, each with 2 numbers, your number of possible combinations are mathematically derived because we are in fact given two variables. The actual answer is not what I’m after but merely to say that it is, in fact, calculable.

To bring my previous derision full circle, we were given two variables. The first was A and the second was U.

My assertion is that Bayes Theory is simple a rule-set by which to write a formula. A formula for a formula if you will. :o)

Kind of redundant in a matter of thinking but a useful teaching tool none the less.

By: BCPower

BCPower — Thu, 09 Feb 2012 12:20:12 +0000

If this is the basis of Bayes Theory than we can simplify all of this to say that, in any given circumstance, if no explicit variables are defined than the outcome of the equation, whether inversely or conversely calculated always equals an equal percentage of the number of circumstances… Or any equal division of the given number of arguments.

In your cancer example, you give explicitly defined variables which makes is possible to calculate an explicit answer.

I take this to mean that Bayes Theory is simply a definition of how to form the equation.

Am I right in my assumption?

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