Hello, I am working on a project devoted to promotions estimation.

My first model was a stan regression with truncated normal distribution on some betas based on the model in the prophet python library. This regression gave expected results, but the warning about divergencies happens after model fitting. So a asked about that in Divergencies with truncated normal.

Then thanks to stan documentation and stan community help in Divergencies with truncated normal I fixed regression by forcing positive influence on some beta during variable initialization in a truncated normal model. The divergencies problem was solved.

But after the fix stan model sometimes doesnâ€™t converge. I get bad Gelman-Rubin statistics, the impact of the promotion takes away some trend influence. It turns out that fitting becomes unstable.

So I tested 3 models on my sales data and made plots with constrained beta influence, trend, seasonality, and other factors influence:

- A regression with positive constraints for the part of betas. Here the impact of the promotion takes away some trend influence. So the model doesnâ€™t converge.

- A truncated normal model. Results are stable, but the warning about divergencies happens. According to documentation and stan community it is an incorrect model.

- A truncated normal model with positive constraints for the part of betas. This is the expected and ideal result. The problem is that sometimes instead of such results in the plot I can get something like in the 1st plot.

It is clear that the cause of such a fitting issue is forcing some beta coefficients to positive during variables initialization. I think that forcing positive constraints violates the premise of an equal probability transition in HMC. Is it right or not? Can we solve the problem and leave constraints in the model?

Iâ€™d appreciate any thoughts on this. Thanks.

Aleksandr