"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