Discussion of "Data fission: splitting a single data point"

Leiner et al. [2023] introduce an important generalization of sample splitting, which they call data fission. They consider two cases of data fission: P1 fission and P2 fission. While P1 fission is extremely useful and easy to use, Leiner et al. [2023] provide P1 fission operations only for the Gaussian and the Poisson distributions. They provide little guidance on how to apply P2 fission operations in practice, leaving the reader unsure of how to apply data fission outside of the Gaussian and Poisson settings. In this discussion, we describe how our own work provides P1 fission operations in a wide variety of families and offers insight into when P1 fission is possible. We also provide guidance on how to actually apply P2 fission in practice, with a special focus on logistic regression. Finally, we interpret P2 fission as a remedy for distributional misspecification when carrying out P1 fission operations.