marc.geddes wrote:
>
> On Aug 29, 5:21 am, Brent Meeker <meeke...@dslextreme.com> 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 don’t 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 Occam’s 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.  That’s 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
> can’t 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, you’re crazy ;)
>   

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

Brent

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