Kurzgesagt - in a nutshell explains perfectly why AI in such Context is really problematic.

Also John Oliver from Last week tonight did a really good video about AI Slop and how many think it's real.

Unfortunately, for the variance on the probability scale, the speed up vanishes.

Thanks for the kind words.
Glad to see that people already account for this in some packages. Not sure whether it helps a lot, but using the direct computations instead of using numerical integration may still speed up things a bit (about 20 times on my machine)

The good news: We provide a simple, correct computation that accounts for this variability, ensuring accurate group-level inferences. This fix is crucial for reliable conclusions in all cognitive models with constrained parameters.

Check out the details to improve your hierarchical analyses!

(e.g. the standard normal CDF) and normal distributions to fit the group-level distribution.
But we cannot simply apply the same transformation to the mean of the real-valued normal distribution to derive the group-level mean on the parameter scale! This ignores individual variability.

If you’re estimating group-level means of constraint parameters, which are fitted with nonlinear transformations, beware that a common approach can produce biased estimates—especially with high individual variability.

For constraint parameters, we often use nonlinear transformations...