Re: Bayes Destroyed?

From: Brent Meeker <meekerdb.domain.name.hidden>
Date: Fri, 28 Aug 2009 23:16:00 -0700

marc.geddes wrote:
>
> On Aug 29, 5:21 am, Brent Meeker <meeke....domain.name.hidden> wrote:
>
>
>> Look at Winbugs or R. They compute with some pretty complex priors -
>> that's what Markov chain Monte Carlo methods were invented for.
>> Complex =/= uncomputable.
>>
>
> Techniques such the Monte Carlo method donít scale well.
>
>
>
They do with Metropolis integration.

>> Actually Bayesian inference gives a precise and quatitative meaning to
>> Occam's razor in selecting between models.
>>
>> http://quasar.as.utexas.edu/papers/ockham.pdf
>>
>>
>>
>
> The formal definitions of Occamís razor are uncomputable. Remember,
> the theory of Bayesian reasoning is *itself* a scientific model, so
> differences of opinion about Bayesian models will result in mutually
> incompatible science. Thatís why Bayes has serious problems. (see
> below for more on this point)
>

And analogical reasoning is computable and doesn't produce any
differences of opinion??

>
>
>> And beliefs do not converge, even in probability - compare Islam and
>> Judaism. Why would any correct theory of degrees of belief suppose
>> that finite data should remove all doubt?
>>
>
>
> So how did people come to believe things like Islam and Judaism in
> the first place? (the beliefs PRIOR to collecting evidence) Bayes
> canít tell you *what* to believe, it can only tell you how your
> beliefs should *change* with new evidence. The fact that you are free
> to believe anything to start with shows that Bayes has major
> problems.
>

The only reasons analogical reasoning seems better to you is that it's a
vague and ill defined method that encompasses anything you want it to.
You are always free to believe anything. Of course Bayesian inference
doesn't solve all problems - but at least it solves some of them.

> Stathis once pointed on this list that crazy people can actually still
> perform axiomatic reasoning very well, and invent all sorts of
> elaborate justifications, the problem is their priors, not their
> reasoning; so if you try to use Bayes as the entire basis of your
> logic, youíre crazy ;)
>

Axiomatic reasoning =/= probabilistic reasoning. Try basing all your
reasoning on analogies.

Brent

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Received on Fri Aug 28 2009 - 23:16:00 PDT

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