Conformal predictive distributions with kernels

Prediction is a fundamental and difficult scientific problem. We limit the scope of our discussion by imposing, from the outset, two restrictions: we only want to predict one real number y R, and we want our prediction to satisfy a reasonable property of validity (under a natural assumption). It can be argued that the fullest prediction for y is a probability measure on R, which can be represented by its distribution function: see, e.g., [5, 6, 8]. We will refer to it as the predictive distribution. A standard property of validity for predictive distributions is being well-calibrated.