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Harry
Posts:
27
Registered:
12/13/04
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Re: The True Meaning of Bayesianism
Posted:
Jun 13, 2006 8:15 AM
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"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
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