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. oracleaide
    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:

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