Control for right skewed DV leading to well fitting posterior

Cool Tweedie model is clearly better. You can improve density overlay plots by adding the following after the plot function call

+ scale_x_sqrt()

and for the interval plots add

+ scale_y_sqrt()

These will apply square root transformation for axes, so that it is easier to see details both near 0 and in the tail.

It seems you are using an old version of bayesplot. You would get better ppc_loo_pit plots with the latest CRAN release, or at least add the following to get the correct diagonal line.

+ geom_abline()

Although the Tweedie model is better the LOO-PIT plot shows it’s not perfect. I did guess correctly that the Posterior PIT-ECDF was too good due to double use of data and flexible model. LOO-PIT plot shows that the Tweedie model is slightly overdispersed compared to the data.