Bayesian Selective Latent Inference for Wastewater-First Influenza Monitoring

Wastewater influenza surveillance can reveal community circulation before clinical reporting, but wastewater alone is not a fully identifiable proxy for human burden. Existing wastewater models assume a fixed evidence set, while generic evidence-acquisition methods treat official surveillance streams as interchangeable costly features. We cast wastewater-first influenza monitoring as a selective decision problem: starting from mandatory wastewater evidence, the system must decide whether wastewater is sufficient, which delayed official stream to query next, and when abstention is the only scientifically defensible action under source ambiguity. We propose Bayesian Selective Latent Inference (BSLI), a principled Bayesian method that maintains a posterior over latent burden and identifiability, certifies answerability through explicit scientific gates, and optimizes query-stop decisions with an exact cost-calibrated Bellman policy. We prove the key variational, answerability, Bellman-optimality, and one-dimensional cost-calibration properties. On a fixed public-data benchmark with 5,933 forecasting episodes and 3,102 source-ambiguity episodes, BSLI improves the matched-budget cost-performance frontier while preserving conservative abstention under source ambiguity.