Help with a simple parameter estimation



I have a problem to solve, where I am trying to constraint posterior based on prior distribution and relations between my random variables. I am starting in edward so I wanted to test a very simple case:
3 random variables (uniform in [0,100], A,B and C that I want to constraint such that A+B+C=100

Sometimes, I also know the value of either B, C or both.
So I’ve tried to implement my problem as bellow:

A = Uniform(low=0.0, high=100.0)
B = Uniform(low=0.0, high=100.0)
C = Uniform(low=0.0, high=100.0)

#Posterior distributions
NToys = 15000
Aq = Empirical(tf.Variable(tf.zeros(NToys)))
Bq = Empirical(tf.Variable(tf.zeros(NToys)))
Cq = Empirical(tf.Variable(tf.zeros(NToys)))

#inference where sum is constrain to 100 and B to 5 and C to 15
inference = ed.HMC(
{A: Aq}, #model
data={B:5.0, C:15.0, SUM: 100.0}) #observation

#print posterior mean and std
print(“A”, Aq.params[14000:].eval().mean(), Aq.params[14000:].eval().std())

Unfortunately, when I run this, I get
A Mean=28.692398 Std=13.735088
which seems too far from the actual solution (A=80) for such a simple problem
What am I missing?

How would you implement my problem for variational inference (I also tried, but the results where even worse :wink: )

Thanks for helping,