The problem of making inferences about real functions of a probability distribution of unknown form is examined in a Bayesian nonparameteric framework. With respect to a general quadratic loss function, Bayes estimates within the class of linear combinations of a given set of functions on the sample space are obtained for general functions on the distribution space. The result is then used to derive Bayes polynomial estimates of the moments of the distribution.
"Approximate Bayes Solutions to Some Nonparametric Problems." Ann. Statist. 3 (2) 512 - 517, March, 1975. https://doi.org/10.1214/aos/1176343081