Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.
|
|
|
|
Re: The True Meaning of Bayesianism
Posted:
Jun 13, 2006 10:30 AM
|
|
Harry wrote:
> "Edward Green" <spamspamspam3@netzero.com> wrote in message
> news:1150175040.701621.269320@i40g2000cwc.googlegroups.com...
> > Nobody asked me, but...
> >
> > I've been thinking about what exactly the so-called Bayesian point of
> > view comprises, and how it differs from the so-called frequentist view.
> > First, some ways they may be alleged to differ but don't:
> >
> > (1) Bayes used a particular equation to update:
> >
> > The Bayesian trope alludes to a fundamental equation, which gives our
> > a-postiori probabilities based on prior probabilities, and an
> > observation. This equation is a standard application of conditional
> > probability and contains no features unique to Bayes.
> >
> > (2) Bayes considers unique, non-repeatable events:
> >
> > This may be more controversial, but I allege there is no real
> > distinction here. Any real event, a particular roll of a particular
> > die, is a non-repeatable event. I can only roll a particular die at a
> > particular time once. As an idealization I may claim that I can repeat
> > this experiment many times with the same die assumed to obey the same
> > distribution, or with a population of identical dies at the same time
> > assumed to obey the same distribution. But I can ideally do this with
> > any unique event: I can abstractly postulate an ensemble of universes
> > conforming to some distribution of initial conditions, even if I only
> > can observe one instance.
> >
> > What then is different? I think it is merely:
> >
> > (3) The Bayesian is willing to guess.
> >
> > Confronted with a unique event, which we ideally want to consider a
> > single instance of an ensemble of identically distributed events, the
> > Bayesian is willing to assign probabilities based upon his sum of prior
> > knowledge in an otherwise undefinable way, e.g. "given my experience
> > with this kind of person, I'd say there is about a 70% chance he is
> > lying". The alternative approach would be to refuse to make any
> > estimates in the lack of almost certain knowledge. This may be
> > satisfying for the purist, but is the opposite of pragmatic: we are
> > often required to act without the luxury of nearly perfect knowledge --
> > including perfect quantification of our ignorance.
> >
> > The question is whether we are willing to accept uncertainty about
> > uncertainty.
>
> Uncertainty about uncertainty must be taken in account of course. My
> question is rather the opposite: what is the true meaning of frequentism.
> Frequentism doesn't tell what a physics experimenter really wants to know -
> a full probability estimation on which a confidence interval may be based.
> An interesting discussion on this subject can be found in
> http://arxiv.org/abs/hep-ex/0002055
>
> Cheers,
> Harald
This is good steerage.
A farce of a farce is a farce.
Perhaps nature has a sense of humor built in.
The joke is on us so it's really not that funny.
If a substrate exists beneath that has coherent rules is there any
guarantee that we as products of this substrate should have direct
access? Quite the opposite; we must not have direct access. Thereby an
empirically driven theory may not break through to the substrate. If
nonobservables in the product space play some part at the lower level
then the divide is widened and a pure theoretical construction will be
the only way.
A procedure with no reversal will also suffer this consequence. So
information loss necessitates the same thinking. Perhaps quantum theory
can be taken as a positive indicator of a substrate.
-Tim
|
|
|
|
