How to specify offset in poisson regression?

The glm-module uses patsy for the formulas, and as far as I know that doesn’t have support for offsets. You’ll have to set up the model manually without the glm module:

with pm.Model() as model:
    ...
    beta = pm.Flat('beta')  # Or whatever is appropriate for your model
    predictor = tt.log(exposure) + beta * x
    pm.Poisson('y', mu=tt.log(predictor), observed=data)