Robust Bayesian exceedance screening for count data

doi:10.1007/s41060-026-01312-5

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Robust Bayesian exceedance screening for count data

2026-10-01

Abdolnasser Sadeghkhani *

DOI：10.1007/s41060-026-01312-5

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Abstract

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Rare-event screening in count data often concerns latent upper-tail risk rather than large observed counts alone. We develop a robust Bayesian procedure whose parameter-conditional tail functional is $$\theta _i(\vartheta ) =\Pr _{\vartheta }(Y_i^{\textrm{rep}}>\tau _i\mid x_i)$$ , where $$x_i$$ is the covariate vector; posterior averaging yields the posterior predictive exceedance probability $$\bar{\theta }_i =\mathbb {E}\{\theta _i(\vartheta )\mid \mathcal {D}_n\}$$ . The working model is negative binomial, with latent-scale robustification and bounded-influence computation used to reduce the impact of excess zeros, isolated large counts, and multiplicative contamination on fitted tail probabilities. The analysis separates posterior tail-risk ranking from formal discovery. Ranking is based on posterior mean exceedance probabilities, whereas multiplicity-controlled selection is obtained through an e-value layer. Under the Bayes-marginal null induced by the same hierarchical model, posterior odds are Bayes factors and hence valid e-values for e-BH false-discovery-rate control under arbitrary dependence. Under a working-model interpretation, the same quantities are treated as evidence scores unless calibrated, and the theory is formulated around a Kullback–Leibler pseudo-true exceedance target. Simulations show improved tail-probability calibration and fewer contamination-driven false discoveries under misspecification, with the expected efficiency loss under clean data. An application to the RAND Health Insurance Experiment illustrates high-utilization screening and identifies a subgroup enriched for large outpatient-visit counts.

Keywords:

Bayesian screening

Exceedance probability

E-values

Negative-binomial regression

Robust inference