{"ID":2851292,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.20742","arxiv_id":"2510.20742","title":"Bayesian Prediction under Moment Conditioning","abstract":"Prediction is a central task of statistics and machine learning, yet many inferential settings provide only partial information, typically in the form of moment constraints or estimating equations. We develop a finite, fully Bayesian framework for propagating such partial information through predictive distributions. Building on de Finetti's representation theorem, we construct a curvature-adaptive version of exchangeable updating that operates directly under finite constraints, yielding an explicit discrete-Gaussian mixture that quantifies predictive uncertainty. The resulting finite-sample bounds depend on the smallest eigenvalue of the information-geometric Hessian, which measures the curvature and identification strength of the constraint manifold. This approach unifies empirical likelihood, Bayesian empirical likelihood, and generalized method-of-moments estimation within a common predictive geometry. On the operational side, it provides computable curvature-sensitive uncertainty bounds for constrained prediction; on the theoretical side, it recovers de Finetti's coherence, Doob's martingale convergence and local asymptotic normality as limiting cases of the same finite mechanism. Our framework thus offers a constructive bridge between partial information and full Bayesian prediction.","short_abstract":"Prediction is a central task of statistics and machine learning, yet many inferential settings provide only partial information, typically in the form of moment constraints or estimating equations. We develop a finite, fully Bayesian framework for propagating such partial information through predictive distributions. B...","url_abs":"https://arxiv.org/abs/2510.20742","url_pdf":"https://arxiv.org/pdf/2510.20742v2","authors":"[\"Nicholas G. Polson\",\"Daniel Zantedeschi\"]","published":"2025-10-23T17:03:17Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}