Re: Axioms of elementary probability

[Greg Meredith <lgreg.meredith@biosimilarity.com>]

David,

Here <http://arxiv.org/abs/math-ph/0508006>'s an arXiv reference for the
"cottage industry" i was referring to.

Best wishes,

--greg

On Wed, May 13, 2009 at 12:59 PM, Greg Meredith <
lgreg.meredith@biosimilarity.com> wrote:

> David,
>
> To my mind there are three presentations of a "theory" of probability. Two
> arrive at essentially the same theory by somewhat different means; these are
> frequentist and Bayesian presentations of "standard" probability theory. The
> third comes from a completely different direction: quantum mechanics. i
> remember when i first encountered the Dirac presentation of QM and the
> interpretation of <a| M |b> as a probability amplitude. My first thought was
> -- hang on, doesn't that come with an obligation to prove that this aligns
> with (satisfies the axioms of) a theory of probability. In attempting to
> work that out for myself, i realized that it didn't; discovered a whole
> cottage industry of people who had made a similar observation; and argued to
> myself that of the various notions of probability put forward, this one
> enjoyed being rigourously employed in physical calculations verified to many
> decimal places.
>
> Best wishes,
>