Distribution-Free Prediction Sets with Random Effects

We consider the problem of constructing distribution-free prediction sets when there are random effects. For iid data, prediction sets can be constructed using the method of conformal prediction (Vovk et al. (2005)). The validity of this prediction set hinges on the assumption that the data are exchangeable, which is not true when there are random effects. We extend the conformal method so that it is valid with random effects.