Narrow posterior

Questions
1

Hi!
I am doing a simple inference problem in which i have the following model:

with pm.Model() as model:
        prior_mu = pm.Normal('prior_mu', mu=mu)
        prior_std = pm.Normal('prior_std', mu=std)
        prior = pm.Normal('prior',prior_mu,prior_std)
   
        pm.Normal('Likelihood', mu=prior, observed=pieces)

where pieces is a signal that is sometimes turned off, and other times has a value quite far from zero. See figure below

image
image1137×871 44.8 KB

The prior mu and sd are the expected value if the pieces-input was constant. After infering this, i get an extremely narrow posterior. Shouldnt the posterior distribution be rather wide as the observed values vary so much?

see figure of the inferred, extremely narrow posterior below.

image
image629×787 3.67 KB

2

I should add that the len(pieces)=310, so there is quite a few datapoints available, the prior std and mu are 5.4, and 55 respectively. This is i guess a rather uninformative prior. The observed data in pieces(see plot above) should in my mind still not make a super confident posterior of about 28? As the observed value varies so much?