Alternative posterior consisteency results in nonparametric binary regression using Gaussian process priors

We establish consistency of posterior distribution when a Gaussian process prior is used as a prior distribution for the unknown binary regression function. Specifically, we take the work of Ghosal and Roy (2007) as our starting point, and then weaken their assumptions on the smoothness of the Gaussian process kernel while retaining a stronger yet applicable condition about design points. Furthermore, we extend their results to multi-dimensional covariates under a weaker smoothness condition on the Gaussian process. Finally, we study the extent to which posterior consistency can be achieved under a general model structure, when additional hyperparameters in the covariance function of a Gaussian process are involved.