Title: Proper Scoring Rules for Survival Analysis. Abstract: Survival analysis is the problem of estimating probability distributions for future events, which can be seen as a problem in uncertainty quantification. Although there are fundamental theories on strictly proper scoring rules for uncertainty quantification, little is known about those for survival analysis. In this paper, we investigate extensions of four major strictly proper scoring rules for survival analysis. Through the extensions, we discuss and clarify the assumptions arising from the discretization of the estimation of probability distributions. We also discuss the relationship between the existing algorithms and extended scoring rules, and we propose new algorithms based on our extensions of the scoring rules for survival analysis.
