Hi,
usually in those cases it is useful to try to isolate the problem by simplifying the model - i.e. does the model work if you have just one block and a single value for C? (it seems your further reply indicates it does) Does the model work if you omit the sigmoid and just assume you have direct noisy observations of C_{s,b}?
Another possibility is that the problem is in the hard constraint:
Hard constraints on parameters like this can pose problems. If you want to express the fact that blockSigmaLogC is unlikely to be very low, it is better to express this as a “soft constraint” by your prior. Hard constraints are usually better reserved for “physical” constraints (e.g. concentration can’t be negative, etc.)
I admit I don’t really see how that arises from the model, but as a heuristic, you could probably reparametrize via something like “overall mean of logC” and “N - 1 differences from mean”, similarly to how you would do in effect coding.
OIne other minor weird thing (likely not a big problem) is:
Since it appears that y cannot be negative, it might make more sense to have a lognormal or gamma observation model.
I assume you plan to estimate other parameters then C at some point. If yes, then I’ll just add that flexible sigmoid models can pose a bunch of challenges on their own. But those tend to manifest primarily when your data do not cover the whole dynamic range, which appears to not be the case in your data.
If yes, then here is a bunch of links to reparametrizations (all of them still have some problems and I am not completely happy about any of those):
- One reparametrization was used in Transcriptome sequencing and multi-plex imaging of prostate cancer microenvironment reveals a dominant role for monocytic cells in progression | BMC Cancer | Full Text, also discussed at Difficulties with logistic population growth model - #3 by martinmodrak
I also wrote about some of the considerations at Hierarchical Gompertz model - #77 by martinmodrak
Best of luck with your model!