  We develop a set of scalable Bayesian inference procedures for a general
class of nonparametric regression models. Specifically, nonparametric Bayesian
inferences are separately performed on each subset randomly split from a
massive dataset, and then the obtained local results are aggregated into global
counterparts. This aggregation step is explicit without involving any
additional computation cost. By a careful partition, we show that our
aggregated inference results obtain an oracle rule in the sense that they are
equivalent to those obtained directly from the entire data (which are
computationally prohibitive). For example, an aggregated credible ball achieves
desirable credibility level and also frequentist coverage while possessing the
same radius as the oracle ball.
