I am trying to build a model that’d ultimately be used to generate predictions for slack/buffer in a process.
For example, in a heating system, the difference between predicted temperature and actual temperature.
The problem is we would like the predicted distribution to follow process specific constraint, specifically we would like the distribution of response y such that p(y > a) ~ b in order to make sure we do not provide too much buffer.
I am at loss how to specify this model. Usually constraints over parameters can be specified as part of prior but not sure how to model this. ( I thought about specifying a hierarchal model as well but still at a loss)
Any pointers or suggestions would be welcome!