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.
best
Robert Dodier