Why doesn't ADVI sample from my prior edges?

Questions v5
6 
from matplotlib.pyplot import hist
from scipy.stats import uniform, norm

fit_mu, fit_sigma = norm.fit(uniform.rvs(size=10_000))
hist(norm(fit_mu, fit_sigma).rvs(10_000), bins=100, ec="k");

image
image552×413 4.97 KB

[Edit:] Hmm MLE includes the edges. The ADVI loss may penalize it more, would need to touble check

How does a 1D uniform look like?