Flexible Conformal Highest Predictive Conditional Density Sets

We introduce our method, conformal highest conditional density sets (CHCDS), that forms conformal prediction sets using existing estimated conditional highest density predictive regions. We prove the validity of the method, and that conformal adjustment is negligible under some regularity conditions. In particular, if we correctly specify the underlying conditional density estimator, the conformal adjustment will be negligible. The conformal adjustment, however, always provides guaranteed nominal unconditional coverage, even when the underlying model is incorrectly specified. We compare the proposed method via simulation and a real data analysis to other existing methods. Our numerical results show that CHCDS is better than existing methods in scenarios where the error term is multi-modal, and just as good as existing methods when the error terms are unimodal.