Hi, thanks for taking the time to look into that! The failure rate is somewhat known, so I can put a tight prior around it. I put Beta(100, 900) prior, and it samples quite well. It seems it’s impossible to infer both failure rate and sensor failure probability at the same time without repeated observations.
That’s exactly my next step. I can check the sensors multiple times for each machine before the failure is registered. The assumption is that as time goes by, more machines will naturally fail, and only the faulty sensors will remain.
The problem is that each unit will now have a different number of observations - after a machine fails, there are no more observations. Is that a problem for the posterior as defined in your model?
Ideally, I probably want a multilevel model for each machine having a separate distribution, but so far, I want it to work as a fully pooled model.
I appreciate your help.