Hi,
there is a recent article
@Article{Fitelson2008ProbabilityCalculus,
author = {Branden Fitelson},
title = {A decision procedure for probability calculus with applications},
journal = {The Review of Symbolic Logic},
year = 2008,
volume = 1,
number = 1,
pages = {111-125},
month = {June}
}
which describes a decision procedure for the elementary theory of
probability calculus.
This is based on the decision procedure for the first-order theory
of the real number --- it would be really good if Maxima had that!
In the article one finds a mathematica-implementation (of the decision
procedure for probability calculus), based on mathematica's incorporation
of the open-source implementation of the decision procedure for the reals:
If Maxima could also incorporate that package, then a lot of power would
be gained: http://www.cs.usna.edu/~qepcad/B/QEPCAD.html.
Oliver
On Thu, Aug 28, 2008 at 05:22:32PM +0200, Jan Ploski wrote:
> "Robert Dodier" <robert.dodier at gmail.com> schrieb am 08/28/2008 04:55:43
> PM:
>
> > On 8/28/08, Jan Ploski <Jan.Ploski at offis.de> wrote:
> >
> > > This is indeed what I meant, i.e. on input
> > >
> > > X : B AND C;
> > > P(A|X) : a;
> > > P(B|C) : b;
> > >
> > > Then ask for the value of P(AB|C) and get a*b in response.
> >
> > > Perhaps you know some other software which supports this sort of
> algebra?
> > > (The closest I can think of is Bayesian network software, but it is
> > > non-symbolic and expects specification of factorized probability
> > > distributions as input.)
> >
> > Well, Bayesian stuff is not necessarily non-symbolic, it's just that
> > there are some special cases for which exact results are known,
> > so those get most of the attention.
> >
> > A while ago I wrote some code for symbolic Bayesian computation
> > in Maxima. The objects of interest are expressions like
> >
> > jpd(AX with cpd = <some-expression>,
> > AY with cpd = <some-expression>,
> > [AX, AY] --> Z
> > with (dom = {0, 1}, cpd = 1/(1 + exp (- (AX * X + AY * Y)))))
> >
> > where jpd, cpd, and dom are abbreviations for joint probability
> > distribution, conditional probability distribution, and domain.
> > Then the game is to compute the marginal posterior distribution
> > for some variable or variables given values of some others.
> > (Of course, solving that problem in general is intractable;
> > the code I wrote can solve some simple problems.)
> >
> > It should be possible to express problems like P(AB|C) in that
> > framework, although it might be kind of clumsy. I'll see if there is
> > a way to express such problems more neatly.
> >
> > I'll post the code and its accompanying paper somewhere.
>
> Robert,
>
> Thanks, I'm looking forward to it. I'd like to have something like that
> for toy/exploration/educational purposes, so it's not bad if it fails on
> big problems. Indeed, it will be interesting to examine why it fails on
> bigger problems when it does.
>
> Regards,
> Jan Ploski
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--
Dr. Oliver Kullmann
Computer Science Department
Swansea University
Faraday Building, Singleton Park
Swansea SA2 8PP, UK
http://cs.swan.ac.uk/~csoliver/