Compare cross-validation schemes for PrO posteriors

Determine whether leave-one-out predictive assessment is more or less appropriate than other cross-validation schemes, and whether alternative cross-validation schemes induce substantially different behavior in predictively-oriented (PrO) posteriors.

Background

The paper introduces the leave-one-out predictively-oriented (LOOPrO) posterior to handle latent parameters and model misspecification in molecular signalling network inference. Its predictive objective evaluates each held-out observation using a posterior predictive distribution informed by the remaining observations. The authors note that this choice is motivated by the latent-variable setting but do not establish whether leave-one-out prediction is preferable to alternative cross-validation or intrinsic-prior constructions.

The unresolved issue concerns both the relative appropriateness of leave-one-out prediction and the possibility that alternative cross-validation schemes could materially alter the behavior, uncertainty quantification, or model weighting of the resulting PrO posterior. Resolving it would clarify whether the proposed LOOPrO construction is robust to the choice of predictive validation scheme.

References

First, it is interesting to understand whether the leave-one-out predictive which we pursued is more or less appropriate compared to other cross-validation schemes \citep{berger1996intrinsic,fong2020marginal}, and indeed whether other cross-validation schemes would induce substantially different behaviour of the \ac{PrO} posterior.

— Overcoming Model Misspecification in Bayesian Inference of Molecular Signalling Networks  (2609.24590 - Li et al., 21 Sep 2026) in Discussion, Section 5, paragraph beginning “From a methodological perspective there are several interesting questions for future work”