Hi there, first off I’d just like to thank y’all for the awesome work you have put in both to PYMC and the extensive guides and documentation!

I am working to build a Gamma-Gamma model of customer spend. I can fit a model using the pm.Potential method similar to the PYMC Marketing method. But I’m curious why a model that is specified as a series of distributions and hyper-parameters doesn’t converge to the same results?

Here is my distribution model:

```
with pm.Model(coords=coord_gamma) as gamma_model_simple:
q = pm.Uniform('q', lower = 1, upper = 10)
y = pm.HalfNormal('y', sigma=3)
v = pm.Gamma('v', alpha=q, beta=y)
p = pm.HalfNormal('p', sigma=5)
z = pm.Gamma('z', alpha=p*gamma_sample_df['num_orders'],
beta=v*gamma_sample_df['num_orders'],
observed=gamma_sample_df['aov'])
gamma_model_simple_trace = pm.sample()
```

Where `gamma_sample_df`

is my user-level observation data of average order value and the `num_orders`

for each customer.

When I run this the model fits with no issues but the parameter estimates for p, q, and y are way off from the pm.Potential model:

```
with pm.Model() as model:
p = pm.HalfNormal(name="p", sigma=10)
q = pm.HalfNormal(name="q", sigma=10)
v = pm.HalfNormal(name="v", sigma=10)
def logp(x, m):
return (
pt.gammaln(p * x + q)
- pt.gammaln(p * x)
- pt.gammaln(q)
+ q * pt.log(v)
+ (p * x - 1) * pt.log(m)
+ (p * x) * pt.log(x)
- (p * x + q) * pt.log(x * m + v)
)
likelihood = pm.Potential(name="likelihood", var=logp(x, m))
```

Unfortunately I can’t share any data, but I was hoping to get some general advice on why the approaches would differ? My ultimate goal is to fit a multilevel model and add customer-specific features to improve the estimates and I’m assuming that would be easier with the fully specific model.

Thanks in advance!