Hans Montcho | Searcharxiv

arXiv2026

Deterministic Leave-One-Cluster-Out Cross-Validation for Multilevel Bayesian Structural Equation Models

We introduce a closed-form, refit-free procedure for leave-one-cluster-out (LOCO) cross-validation in multilevel Gaussian Bayesian structural equation models (SEMs), together with predictive scoring of every nested submodel. Conditional independence of clusters given the parameters expresses the cluster-deleted posterior as a functional of the full posterior. The LOCO predictive density is then a harmonic mean of the cluster likelihood, computable from a single fit in INLAvaan, the integrated nested Laplace approximation package for Bayesian SEM. We evaluate the harmonic-mean expectation in closed form through a fully exponential Laplace approximation of the reciprocal cluster likelihood under a Gaussian posterior; candidate structural restrictions follow by Gaussian conditioning of the same Laplace summary. The resulting Taylor elpd (expected log predictive density) scores are fully deterministic, requiring neither refitting nor Monte Carlo sampling, so the variance pathology of the naive harmonic-mean estimator does not arise. A direct-sum decomposition of the compound-symmetric cluster covariance makes the cost independent of cluster size, orders of magnitude below brute-force refitting. We validate against brute-force refits and Markov chain Monte Carlo in simulation, and illustrate the procedure on school-safety climate in PISA 2022 and on 16 candidate structures linking personality and well-being in the MIDUS sibling sample.

stat.ME↗

arXiv2026

Coherent information deletion: Bayes' theorem and generalized Bayesian unlearning

Bayes' theorem admits an information-processing interpretation due to Zellner (1988): under the Shannon-information criterion, the posterior is the unique rule that processes prior and data information without information loss. We revisit these ideas, but from the perspective of information deletion. Given a posterior based on a complete dataset, what distribution should replace it when a subset of the data is removed? We define information deletion using the same information conservation principle as Zellner (1988), and show that the optimalpost-deletion distribution is exactly the leave-data-out posterior. We then extend the framework beyond likelihood-based inference from Bayes to the generalized Bayesian updating of Bissiri et al. (2016) based on loss functions. We introduce a sequential coherence requirement for deletion, under which, removing two pieces of information jointly is equivalent to removing them successively. The resulting coherent deletion rule exactly recovers the generalized Bayesian posterior based only on the retained data. Restricting these optimization problems to variational families yields corresponding formulations of variational Bayesian and generalized Bayesian unlearning.

stat.ME↗