Bayes' theorem BUNKERIZED - You are busted, Mr. Bayes^^

This post is a continuation of the articles about the Bayes' theorem previously posted by Paskal on this Blog and the blog of Ascot Project.

The Bayes' theorem is indeed a typical example of how we, at BunkerSofa, approach dogma and technological paradigms currently used.
In particular, we like to spot logical fallacies as well as technical misinterpretations and argue why they are wrong and can lead to systems not working at all.
The act of spotting, closing up and criticizing using Bunkersofist values ("putting into quarantine" if I dare say) is what I want to call to BUNKERIZE.

Also, very important to be aware of. Bayes' theorem is heavily used in the field of Speech Recognition, Information Retrieval, Natural Language Processing and Anti-Spam methods; So I think it is all the more crucial to question its validity.

So let's get to the point; what on earth is wrong with the Bayes' theorem , a solid and very respected theorem that has hardly ever been questioned?
Well, apart from that it's based on a triviality, nothing on the mathematical standpoint; But when it comes to its usage for example in the Computer Science field, problems arise;


1) Triviality of the Bayes' theorem:

First let met remind you what the theorem is about.
The famous theorem only states that:
P(A/B)=P(B/A)*P(B)/P(A)

where A and B are 2 given events and P a probability.
So, in fact, the theorem can almost be reduced to stating that
A & B = B & A

Why?
Well, let me demonstrate the Bayes theorem again then in 3 lines.

a) As Bayes defined, I define:
P(A/B)=P(A&B)/P(B)
P(B/A)=P(B&A)/P(A)

b) But A&B = B&A so P(A&B)=P(B&A)
c) Then P(A/B)=P(B/A)*P(B)/P(A)

So all it does is relying on the fact that A&B = B&A is true.
This is indeed mathematically true because that's the very definition of "&", a symmetric relation.


2) Misinterpretations of the Bayes' theorem:

Well, how you interpret (A&B = B&A) is the source of all problems.
(A&B = B&A) is a binary formula that does not take Time into account at all, namely it is non-temporal, that is, Time just does not exist inside it.

The question then is: how do you interpret what it means for the real world, in practice where Time exists and flows?
To understand the intricacies, let's focus in particular on (A&B) and speculate on its meaning.

a)Is it A immediately followed by B ?
If so, followed within how much time?

b)Does A have to simultaneously occur at the same exact instant as B?

Well, the answer is neither a) nor b) for the very reason that the theorem does not consider the flow of Time.


- So if you want to apply the theorem for the real world, you have to consider cases where a) and b) are confounded so that you do not have to be confronted with the interpretation problem;
And then it's not big deal. Bayes works perfectly but the cases are restricted.

Consider the example: A="To be a girl" and B="To wear a dress".
Another easy one is: A="The glass is filled" and B="To be poured with Red Wine".

As you may have noticed, these 2 examples are about events that are sufficiently macroscopic enough for the human brain to consider them non-temporal.
And this is the condition for the Theorem to be applied correctly in the real world.

The condition is the following:

You have to consider only situations where the events are such that it does not matter whether A is prior or subsequent to B.

- But apparently, many computer scientists haven't not understood this crucial condition well.
They are currently applying it quite vaguely for Speech Recognition where they claim without much care such, statements like (A&B)=(B&A) where for example, A=("utterance of the phoneme "bu") and B=("utterance of the phoneme "zz").

Obviously, ("bu"&"zz") is not the same as ("zz"&"bu")...


That's pretty much it for now!
Bayes' theorem has just been BUNKERIZED☆
You are busted, Mr.Bayes!^^


I hope you will take this quarantine of this virus of the mind (i.e. Bayes' theorem) to study it and know how to use it more carefully in your applications.


Also, this may be a new movement at BunkerSofa and a fun application of the Bunkersofist philosophy, namely we could Bunkerize viruses of the mind that are dangerous, stick to the human brain and are based on fallacies.

Should we call ourselves the MemeBusters?^^