Bayes’ Theorem

There is a very long and somehow windy—if often funny—introduction to Bayes’ theorem by a researcher in artificial intelligence. In particular, it contains several Java applets that shows how intuition about posterior probabilities can be wrong. The whole text is about constructing Bayes’ theorem for simple binomial outcomes with two possible causes. It is indeed funny and entertaining (at least at the beginning) but, as a mathematician, I do not see how these many pages build more intuition than looking at the mere definition of a conditional probability and at the inversion that is the essence of Bayes’ theorem. The author agrees to some level about this “By this point, Bayes’ Theorem may seem blatantly obvious or even tautological, rather than exciting and new. If so, this introduction has entirely succeeded in its purpose.” Quite right.

When looking further, there is however a whole crowd on the blogs that seems to see more in Bayes’s theorem than a mere probability inversion, see here and there and there again for examples, a focus that actually confuses—to some extent—the theorem [two-line proof, no problem, Bayes' theorem being indeed tautological] with the construction of prior probabilities or densities [a forever-debatable issue]. The theorem per se offers no difficulty, so this may be due to the counter-intuitive inversion of probabilities as the one found in the example of the first blog. But the fact that people often confuse probabilities of causes and probabilities of effects—i.e. the right order of conditioning—does not require a deeper explanation for Bayes’ theorem, rather a pointer at causal reasoning!

18 Responses to “Bayes’ Theorem”

  1. savitha bhandary Says:

    i need code for bayes theoren in java programming language

    • @savitha: I am afraid I do not understand your question, in that Bayes theorem does not need an advanced code when all four elements of the equation are available… What do you mean?

  2. radhie.com…

    [...]Bayes’ Theorem « Xi'an's Og[...]…

  3. [...] could not keep track with the mechanics behind it! In the afternoon, Michael Goldstein told us why Bayes theorem does not work (not that I agree with him on that point!), Peggy Series explained how, [...]

  4. [...] I managed to have a glaring typo in my slides, pointed out by Susie Bayarri: Bayes theorem was written [...]

  5. [...] baccalauréat my son took on Tuesday, the probability problem was a straightforward application of Bayes’ theorem. Given a viral test with 99% positives for infected patients and 97% negatives for non-infected [...]

  6. [...] signaled a series of blogs and videos by IBM Netezza about Thomas Bayes and the consequences of his theorem. Which made me realise this was indeed the 250th anniversary of his death, and that maybe we (as a [...]

  7. [...] perception of Bayesian statistics (if strong on the militant side!). Jaynes did not think much of Bayes himself (an amateur!, on page 112), considering that Laplace had done much more to establish [...]

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

Follow

Get every new post delivered to your Inbox.

Join 667 other followers