Home > My Original Post > Bayes’ Theorem Visualization by Venn Diagram

## Bayes’ Theorem Visualization by Venn Diagram

Almost all of the math books only give logical explanations of Bayes’ Theorem. Sometimes it is hard to intuitively understand how it comes . I’m trying to visualize the theorem by Venn diagram. Actually, it is a very simple concept.  I don’t understand why don’t these math book authors put such a picture into book to help people understand, or they don’t want their book appears easy? I took probability courses in high school, undergrad and grad, but I’ve never seen a similar approach to elaborate this problem.

Bayes’ Theorem

$P[A_j|B] = \frac{P[B|A_j] P[A_j]}{P[B]}$

There are several events $A_j$ are mutually exclusive and divide universal space S into several parts.

We assume event B occurs when  $A_j$ happen.

Assume we already know $P[A_j], P[B]$ and $P[B|A_j]$, then we can get $P[A_j|B]$.

$P[B|A_j]$ is a priori,

$P[A_j|B]$ is a posteriori.

Categories: My Original Post
1. December 27, 2012 at 7:43 pm

I like the idea (and colours).
I came up with a Venn Pie Chart – a pie chart with overlapping sectors – to show raios between sets:
http://oracleaide.wordpress.com/2012/12/26/a-venn-pie/