  We consider heteroscedastic nonparametric regression models, when both the
mean function and variance function are unknown and to be estimated with
nonparametric approaches. We derive convergence rates of posterior
distributions for this model with different priors, including splines and
Gaussian process priors. The results are based on the general ones on the rates
of convergence of posterior distributions for independent, non-identically
distributed observations, and are established for both of the cases with random
covariates, and deterministic covariates. We also illustrate that the results
can be achieved for all levels of regularity, which means they are adaptive.
