Linear regression with log-normal model: posterior predictive is quite off

[han.xiao]

Thanks for your reply!

I updated the above example by adding random noise to the observed responses.

Notebook

However, the aforementioned issue persists:

1. predictions tend to be lower than the observed values, if trace.posterior_predictive is used for inference
2. meanwhile, predictions align better with observed values if we operate on the posterior samples and do the calculation outside of the model