A Bayesian global Fréchet regression method is introduced via a Fréchet Bayes rule that reduces the problem to scalar tasks, allows prior-data interpolation, and remains valid under moment conditions using weak conditional expectations.
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Derives error bounds on the root prior-preconditioned Hessian, posterior covariance, and mean for a Petrov-Galerkin reduced-order model, with exact posterior recovery at the intrinsic dimension.
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Bayesian Global Fr\'echet Regression via Weak Conditional Expectations
A Bayesian global Fréchet regression method is introduced via a Fréchet Bayes rule that reduces the problem to scalar tasks, allows prior-data interpolation, and remains valid under moment conditions using weak conditional expectations.