I’m new to pymc. Thank you for your great efforts for this amazing library.

Now I’m learning the behavior of custom distribution defined by `pm.DensityDist`

in v4.1.3. For this, I made two equivalent simple gaussian models as follows.

Both models coverge well, but the latter custom model shows larger value of estimation for `sigma`

, probably due to my misunderstanding of the usage of `pm.DensityDist`

. Could you specify any reasons?

Any suggestions are welcome. Thank you in advance.

```
import arviz as az
import numpy as np
import pymc as pm
import aesara.tensor as at
RANDOM_SEED = 8927
rng = np.random.default_rng(RANDOM_SEED)
#create data from true distribution
data = rng.normal(loc=5,scale=2, size=1000)
print( data.mean(), data.std() )
#1st model using pm.Normal()
model_builtin = pm.Model()
with model_builtin:
mu = pm.Normal("mu", mu=0, sigma=5)
sigma = pm.HalfNormal("sigma", sigma=5)
obs = pm.Normal("obs",mu=mu,sigma=sigma, observed=data)
idata_builtin = pm.sample()
#2nd model using pm.DensityDist
def _logp(obs, mu, sigma):
z = (obs-mu)/sigma
return -at.sum(z**2) / 2
model_custom = pm.Model()
with model_custom:
mu = pm.Normal("mu", mu=0, sigma=5)
sigma = pm.HalfNormal("sigma", sigma=5)
# obs = pm.Normal("obs",mu=mu,sigma=sigma, observed=data)
obs = pm.DensityDist("obs", mu,sigma, logp=_logp, observed=data) #only changed here
idata_custom = pm.sample()
#check posteriors
display(pm.summary(idata_builtin))
display(pm.summary(idata_custom))
```