Bayesian Prediction under Moment Conditioning
arXiv:2510.20742
The paper develops a Bayesian framework for prediction when only moment restrictions are available, using Kullback‑Leibler projection to define a conditional law for blocks of an exchangeable ensemble and establishing Gaussian approximations and convergence results.
Abstract
Moment restrictions specify a class of laws, not a predictive model. We obtain one by conditioning an independent sample from a reference law on its empirical moments, and define prediction as the law of a fixed block selected from that conditioned ensemble. On a finite partition this law is an exact mixture over empirical types. Under exact feasibility and lattice regularity, the mixing law has a Gaussian limit on the feasible tangent space, governed by the reduced Hessian, and the selected block approaches independent sampling from the Kullback-Leibler projection. A separate finite-sample bound gives the same product limit for general real-valued restrictions without lattice assumptions. Refinement recovers the projection on the original sample space. Parameterizing the projected family produces a predictive product criterion with a local inverse-covariance expansion, connecting the construction to generalized method of moments.
42 pages, 7 external figure files. Main text and appendix combined. v4 aligns the preprint with corrected fixed-chart localization assumptions and constants, strengthened refinement hypotheses, added an exact finite-chart collapse calculation and updated the partition-sizing calibration; reference metadata, estimator terminology, and source attributions were also checked and corrected