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By Ismaël Castillo, Richard Nickl.

Annals of Statistics 41(4), 1999–2028. DOI: doi.org/10.1214/13-AOS1133 . Section 2.3.1: inference on linear functionals and required regularity; conjugate product-prior formulas and explicit bias condition in the wiki are independent calculations.

Richard Nickl coauthored nonparametric Bernstein-von Mises theorems with Ismaël Castillo for the Gaussian white noise model. Their work explains when Bayesian credible sets can also have asymptotically correct frequentist coverage probability. The result connects the limiting posterior geometry with efficient inference on an unknown function, rather than only a fixed finite-dimensional parameter.^[ref]