Compatibility-based Bayesian inference: asymptotic limits, variational principles, and Wasserstein geometry
基于相容性的贝叶斯推断:渐近极限、变分原理与 Wasserstein 几何
Approximate Bayesian Computation (ABC) replaces intractable likelihood evaluations with comparisons between observed and simulated data. We develop a measure-theoretic formulation of discrepancy-based Bayesian inference in which compatibility is encoded through nonnegative weights. For vanishing thresholds, we establish convergence of the corresponding posterior distributions in total variation. In the large-sample regime, we identify conditions under which the posterior…