I would like to know what's the exact way to obtain the conditional probabilities of node having multiple independent continuous random variables as its parent.
Say something like a Noisy OR gate model, with multiple parents of continuous random variable types.
The samples, I stumbled upon so far (for Noisy OR gate) where explained using discrete binary random variables, but my interest mostly lies on achieving similar outcomes with one or more continuous & random as inputs?
Let me explain with a simple example from Google results. A simple study says Bronchitis (B), Tuberculosis (T) and Lung cancer (L) causes Fatigue (F). It also says probability of B -> F = 0.6, T -> F = 0.7, L -> F = 0.8. with this information if we had to find out P(F|B,T,L), then the way to do this is find out
P(no F|B, T, L) = (1-0.6)(1-0.7)(1-0.8) = 0.024
then P(F|B,T,L) = 1 - P(no F|B, T, L) = 0.976.
In the above case all the causation random variable are of type discrete. In case if we add a continuous random variable say age to the scenario.
B -> F = 0.6, T -> F = 0.7, L -> F = 0.8
and if age (a) is
a <= 30 -> F = 0.1,
30 > a <= 50 -> F = 0.2, and
a > 50 -> F = 0.7.
Then if I had to find out P(F|B,T,L,30 > a <= 50), then what should be logic to find it out?
If just look at the example without considering age, we never know the joint probability distribution of of two or more individual events, but the final conditional probability of F given B,L & C has happened at ones is obtained using the individual probabilities of B,L & C.
Similarly I would like to know the way to compute P(F|B,T,L,30 > a <= 50)? Where 'a' is a discretized continuous random variable to ease the analysis.