Hi all,

I am trying to figure out what does the NUTS sampler do when it is not given an observed data. Intuitively I’d expect it will work like just a regular numpy random number generator, but this seems not to be the case. Here is a quick demo:

```
joint_model = pm.Model()
var = np.full(400,1e-6)
var[0:10] = 300
with joint_model:
a = pm.Normal("a", mu=0, sigma=100)
b = pm.Normal("b", mu=0, sigma=var)
tr = pm.sample(draws=50,n_init=20,tune=20)
plt.hist(np.array(tr.posterior.stack(sample=["chain", "draw"])["a"]),bins=50)
plt.show()
```

Here, the result for “a” looks nothing like a normal distribution that I’d expect (instead, it is peaked at some location not close to the mean). However, things look better if say we change the sampling parameters to, say,

```
tr = pm.sample(draws=50,n_init=500,tune=500)
```

I am wondering why is this happening. Can we use/interpret pm.Normal as an RNG? Does the sampler still impose some likelihood function when not given an observed data? Thanks a lot in advance!