Probability that a given constraint is observed

Questions
#1

Hi,

This is general modeling question. I have a model with 2 poisson distributed variables, P1 and P2, and my observed data reflect the belief that P1 is greater than P2. How can I model something like this, i.e.:

p(P1>P2)=observed

?

Thanks

#2

This is a bit tricky as I dont know if the log likelihood function of p(P1 > P2) is easily expressed.
If you can find out the logp function for this you can write it as a DensityDist. Otherwise, you will need some likelihood-free inference approach, which we are currently working on implementing it.

#3

Hi,

Thanks. Since observed is in [0,1], I tried adding the potentials

(P1-P2)*observed

or

(P1>P2)*observed

but I have the feeling this is completely wrong (I’m a newbie) :slight_smile:

Could you please point me to some paper about the likelihood-free inference approach you mentioned?

In the past I helped developing something called Probabilistic Constraint Programming, I wonder if it is related and how.

Thanks
Marco

#4

You can have a look at the example in https://github.com/elfi-dev/elfi

#5

Many thanks!