Re: [MLUG - DISCUSSION] statistical inference

["Jonathan King" <EMAIL:PROTECTED>]

On 6/5/06, Mike Miller <EMAIL:PROTECTED> wrote:
> On Mon, 5 Jun 2006, Stephen Montgomery-Smith wrote:
>
> > Quite likely I am going to put a lot of thought into this problem next
> > year (now I have other projects), but one possibility I am considering
> > is that the Kolmogorov laws of probability don't always apply.
>
> Apply to what?  Kolmogorov's "laws"  are axioms and they create an
> imaginary world in which they always apply.  In science we try to
> construct an imaginary world (model) that mimics the real world.  It would
> be convenient to construct a model where you can use Kolmogorov's axioms,
> but I suppose it isn't necessary.

I think you may have missed a message where Stephen backed off from
this a bit.  I'm not exactly sure what he had in mind, but I think
there is an interesting issue in Bayesian inference that has to do
with using (initially) improper priors and somehow then getting back
something that obeys the axioms.  Right now, it's just one of those
things you do, but he may be right that there is something deeper
going on here.  It has always struck me as funny that Bayes is
supposed to go from one belief state to an updated one, and these all
follow the axioms of probability except for the first one, which might
not.

But that's not my area of expertise.  Today, my area of expertise is
tweaking plots in R for a talk I have to give on Thursday...

jking

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