Here is an example:

I have a discrete binary node X, and an observation y which has a continuous distribution with density f(y | z) given a discrete network variable Z. I want to define the distribution of X | Z using the distribution of y. We may think of y as a fixed quantity that is used when building the network.

If I simply want

P(X = 1 | Z = z) = P(Y < y | Z = z),

I think that this could perhaps be done by instead making X an interval node with states [-inf, y] and [y, inf].

Now, sometimes I want to let

P(X = 1 | Z = z) = f(y | z)/k

and then P(X = 0 | Z = z) = 1 - P(X = 1 | Z = z).

This is more difficult for two reasons.

The first reason is the essence of my question: I need to be able to evaluate the density f in this arbitrary point y.

The other reason is that I need to identify a constant k so that f(y | z)/k becomes a well defined probability. When I create tables by hand, I may do this simply by taking k to be max_z{f(y | z)}. I suspect that this will not be possible, because the expression is naturally defined for only one state z of Z.

I hope that my question makes sense. Hugin already computes everything I need like a charm. I'm simply exploring other ways of doing the same thing

Therese