Homeostasis phenomenon in conformal prediction and predictive distribution functions

Conformal prediction is an attractive framework for that distribution free. In this article, we study in details its homeostasis property under a general regression setup and also introduce the concepts of upper lower predictive distributions curve to establish connections left-, right- two-tailed hypothesis testing problems as well developments confidence distributions. The very attractive, since it states some conditions results remain valid even if model used learning completely wrong. We show explicitly why holds model-based explore boundary when breaks down. Beside typical assumption conformal response covariate pairs ( y , x ) all subjects are iid distributed, classical setting which design fixed with given (non-random) covariates . trade-offs among accuracy, efficiency discussed, leading emphasis more efforts on developing better models.