  Examples with bound information on the regression function and density abound
in many real applications. We propose a novel approach for estimating such
functions by incorporating the prior knowledge on the bounds. Specially, a
Gaussian process is first imposed on the regression function whose posterior
distribution is then projected onto the bounded space. The resulting projected
measure is then used for inference. The projected sample path has closed form
which facilitates efficient computations. In particular, our projection
approach maintains a comparable computational efficiency with that of the
original GP. The proposed method yield predictions that respects bound
constraints everywhere, while allows varying bounds across the input domain. An
extensive simulation study is carried out which demonstrates that the
performance of our approach dominates that of the competitors. An application
to real data set is also considered.
