Comments on Bunkersofism: Bayes' theorem BUNKERIZED - You are busted, Mr. Ba...

1) Thanks for the detailed comment; Looking backwa...

2010-10-27T20:36:53.934-07:00

1) Thanks for the detailed comment;
Looking backwards at this post,
indeed this passage
"- 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")... "
is inappropriate since it is not backed by references;

http://en.wikipedia.org/wiki/Hidden_Markov_model is the simplest type of DBN and it seems indeed to cope well with the "time" issue by considering probabilities of transition.

2) "On the other hand, mathematics is a field not particularly susceptible to memes. If a long-lived theorem could be disproven or discounted in an afternoon by a blogger, a mathematician would have published such a result long ago because it would have made her famous."
is however not an argument to prove that some theorems can't be false.

>1) Triviality of the Bayes' theorem All y...

2010-07-31T13:27:46.573-07:00

>1) Triviality of the Bayes' theorem

All you have done here is shown the derivation of Bayes' theorem in reverse. As seen here http://en.wikipedia.org/wiki/Bayes'_theorem#Derivation_from_conditional_probabilities

>So all it does is relying on the fact that A&B = B&A is true.

In general, you cannot show the "triviality" of any mathematical statement by reducing it to another. In fact, all theorems are based on simpler, previously known facts. Instead a theorem must be judged first on correctness, and second on how useful it is in proving other theorems (or how useful it is in applications). Bayes' Theorem is correct, as you have shown, and it has been used extensively in many fields.

>(A&B = B&A) is a binary formula that does not take Time into account at all [...]

The only issue here is how one defines their random variables A and B. In domains where time is an issue it is accounted for. Commonly you will see random variables subscripted by 't' if time is at play.

>Bayes works perfectly but the cases are restricted.

There are no restrictions on Bayes' theorem, as you proved yourself. Symmetry (p(A,B)=p(B,A)) is true for all A and B which led directly to the derivation.

>They are currently applying it quite vaguely for Speech Recognition [...]

Look at any speech recognition paper, and you will see time accounted for. One of the tools most commonly used in speech recognition is the Dynamic Bayesian Network, which is a model specifically designed for temporal domains. Looking in my graphical models textbook (Probabilistic Graphical Models; Daphne Koller & Nir Friedman) there is an entire section on temporal models.

>virus of the mind (i.e. Bayes' theorem)

For perspective, Bayes' theorem has been around since 1763. Yes the Ptolemaic system was around for a long time, but you can blame that on the scarcity of quality astronomical observations. On the other hand, mathematics is a field not particularly susceptible to memes. If a long-lived theorem could be disproven or discounted in an afternoon by a blogger, a mathematician would have published such a result long ago because it would have made her famous. In math there aren't many forces that work to perpetuate falsities, because a mathematician could make a career out of finding and eliminating those falsities.

I do think there is a place for skepticism of science, and science journalism. There is such a thing as "bad" science, an obvious example being funding bias. Just be aware that a lot of facts in science have rightfully withstood the test of time. And in any case, do your research. It wouldn't have taken much effort for you to find that probabilistic modelling folks have an entire subfield devoted to temporal models.

If you are interested in legitimate critiques to the use of Bayes' theorem in practice, you could take a look at this: http://www.stat.columbia.edu/~gelman/research/published/badbayesmain.pdf To summarize, Bayes' thm. is often applied like this [see http://en.wikipedia.org/wiki/Bayesian_inference#Posterior_distribution_of_the_binomial_parameter for another example]:

D - data
H - hypothesis

P(H|D) = P(D|H)*P(H) / sum_H { P(D|H)*P(H) }

That is, you wish to evaluate a hypothetical model H using some training data D. Bayesian learning allows you to compute P(H|D) from P(D|H) which can be easy by design. The nasty issue is P(H). This is called the prior distribution over hypotheses. How could you possibly know the probability of a hypothesis when disregarding any evidence? Usually P(H) is chosen to be a conjugate prior which is purely out of computational convenience. The consequences of this have been studied, yet it remains controversial. But in countless applications it (provably) works just fine. It's better than nothing! And there are bright young folks today doing their PhD work in Learning Theory, and hopefully they can come up with something better.

A trusted theory does not make it valid and right....

2010-07-31T00:42:59.636-07:00

A trusted theory does not make it valid and right.
Please remember the Ptolemaic system which had been used for more than one thousand years.
http://en.wikipedia.org/wiki/Geocentric_model#Ptolemaic_system

Tks.

Mr Anonymous, show me where the reasoning is false...

2010-07-30T18:51:19.938-07:00

Mr Anonymous, show me where the reasoning is false and prove me wrong. txs.

Bayesian statistics has always been controversial....

2010-07-30T11:59:34.399-07:00

Bayesian statistics has always been controversial. Your critique is vacuous. If you actually did your research you would find that REAL criticisms of Bayesian statistics are subtle and complex, and no single blog post is going to "debunk" a well established field. Philosophical considerations aside, Bayesian statistics has for decades proven itself an invaluable tool across disciplines. Why not, instead of blogging about science like you know something about it, go to school and do REAL SCIENCE and see if you can make an actual difference.

もう直ぐ日本語訳も出る、もう少々お待ち下さい。

2009-10-26T11:09:46.356-07:00

もう直ぐ日本語訳も出る、もう少々お待ち下さい。

Amazing graphical illustration, julien. Amazing Bu...

2009-10-26T11:09:12.693-07:00

Amazing graphical illustration, julien.
Amazing Bunkersofigram.

I do think that that post is the best illustration so far of what bunkersofism consists in.

Fighting the old paradigms.

Questioning things that are taken for granted and reinventing things.

It is like Einstein that doubted the mechanical view that Newton had regarding the universe.
If concepts, or theories remain too long in people's brains, they become viruses for the mind and therefore they ve got to be quarantined, that is "bunkerized"!