High number of divergent transitions in ODE model with explicit constraints



Last example


Thanks. I thought we are talking about the actual stan model in terms of transformation.

I have done the transformation and plotted the results:

all_transformed.pdf (10.3 KB)


Somehow the k is diverging when it is low. Could this be due the hard boundary (lower=0)

Do you need to limit k (maybe try without limits or at least without the lower limit)? It’s going into 2^k. What is the description for k?

P.s. recently @Bob_Carpenter wrote a blogpost concerning uniform priors. http://andrewgelman.com/2017/11/28/computational-statistical-issues-uniform-interval-priors/


I just tried that and divergence increased from 41 to 199 transitions.

It describes clonal expansion and thus k should not go below 0 .

I’ll have a look at that.

Do you have any intuition what else could be going wrong here?


Some of the posteriors seem to be “cut” at 0 when looking at the density plots. Using uninformative uniform prior such as U(-1,1) lead to all post warm-up transitions to be divergent and the posterior look not as expected(I know the true value since I use simulated data).


Oh yeah, like @ahartikainen said, this is definitely not a great thing.

Is it possible to use more simulated data and maybe that’d tighten up the posteriors and get you away from the boundaries? If the divergent transitions go away then that’ll tell you something.

Is it possible to post the R code to play with this?


Increasing datapoints reduced divergent transitions form 41 to 10. Which reduced further to 9 when I increased adapt_delta to 0.9 but when I increased warmup and sampling to 1000 steps each and also increased adapt_delta to 0.99 I ended up with all post-warmup transtions being divergent.

Lastly, adding further datapoints somehow increased divergence again but I am currently looking why that could be.


You could also try playing with adding tight priors around the right answer instead of the uniform ones to see if that changes anything.

But my advice is getting a little vague and drifty at this point :D. I’ll be back at my comfy desk in a few days and wouldn’t mind running the code a few times then if it’s easy to post the R code here.