Jesse,
I appreciate your help!
Your suggestions all make sense.
Initially, I thought the negativity in predictions was the problem. Also, because of the negative mass there, it seems the overall density shape is not consistent with the observation.
I am using either lognormal or truncated normal to sample positive values for “Lambda”, which is my key latent variable. Theoretically, as long as “Lambda” is positive, the predicted value (equivalent to measurement Y) should also be positive. This means if you take any values from the sampled Lambda and multiply them by “K” (all positive values), you always get positive values (i.e., Y_mean = K*Lambda_mean).
Because I am trying to infer “Lambda” values rather than predictions of Y values, maybe PPC may not matter much as long as there is reasonable consistency between predicted and observed Y. As a side, I am not sure how exactly the “pm.sample_posterior_predictive” function works; I’ve looked at the source code, but it wasn’t easy to follow.
I will look into this more.
Again, thanks for the help!
- Seongeun