  We propose Bayesian extensions of two nonparametric regression methods which
are kernel and mutual $k$-nearest neighbor regression methods. Derived based on
Gaussian process models for regression, the extensions provide distributions
for target value estimates and the framework to select the hyperparameters. It
is shown that both the proposed methods asymptotically converge to kernel and
mutual $k$-nearest neighbor regression methods, respectively. The simulation
results show that the proposed methods can select proper hyperparameters and
are better than or comparable to the former methods for an artificial data set
and a real world data set.
