On 2013-02-16, James Cloos <cloos at jhcloos.com> wrote:
> Random Variable.
OK. I've worked on stuff like that off and on (mostly off) for some
time. I noticed recently that this topic seems to be getting some
traction under the name "probabilistic programming" (see e.g. [1]).
From what I can tell, the usual approach is to compute posterior
distributions via Markov chain Monte Carlo. I don't know if other
numerical approximations have been considered, and I don't know if
exact methods have been considered. For what it's worth, for my
dissertation [2] I worked with exact, non-symbolic methods (yes, it was
painful) and numerical approximations other than MCMC. More recently, I
formulated some stuff in Maxima and wrote it up; hmm, that reminds me,
I should submit that to the next probabilistic programming workshop (it
has already been rejected by another conference).
The general approach that I'd like to push is to use symbolic inference
to get as far as we can, then resort to numerical approximation. In the
most general case, I suppose only MCMC is workable, but I believe there
are interesting special cases that can be handled better by symbolic or
symbolic + numerical methods, and/or by numerical methods other than
MCMC. I think Maxima is an interesting environment for this work because
(waving hands here) it can handle the symbolic part, then generate a
program to carry out the numerical approximation.
Sorry if I'm repeating myself; this is just my standard rant which I
trot out whenever it seems appropriate to air it.
best,
Robert Dodier
[1] http://probabilistic-programming.org/wiki/Home
[2] http://riso.sourceforge.net/docs/dodier-dissertation.pdf