NaN values are obtained even if the data generating process is directly dependent on a Poisson distribution. In the following code, I anticipate that the ed.inferences.MAP should give the same result as MLE.
from edward.models import Poisson
N = 10
lmb = tf.Variable(0.0, dtype=tf.float32)
x = Poisson(rate=tf.ones(N) * lmb)
inference = ed.MAP(data = {x: X_train})
inference.run()
sess = ed.get_session()
print (sess.run([lmb]))
It prints [nan]. What do you suggest should be done in this case?