Posterior Drift Profiles for Adaptive Generalization and Concentration

Reusing data to choose and evaluate a model or query can introduce selection bias and alter sampling fluctuations. We introduce posterior drift profiles, which measure the largest Wasserstein displacement of a data law under log-likelihood perturbations of bounded sensitivity. A profile bound has two uses: its value supplies the selection-bias allowance in transferring sample accuracy to population accuracy, while its integral yields concentration around the fresh-data mean, including after stable selection. Both guarantees use the original law's profile, so the same calculation can serve different selection procedures and statistics. We prove exact tensorization for product laws under additive metrics, even when selection induces posterior dependence. Explicit calculations cover bounded queries, sampling without replacement, and unbounded Lipschitz queries under metric privacy. The nonlinear Gamma profile shows why the profile's shape matters: increasing likelihood sensitivity can enlarge both bias and fluctuation bounds. A one-sided extension also accommodates asymmetric, dataset-dependent sensitivity.