ABSTRACT
In this chapter, we discuss the details of the idea on using Gaussian process priors for a Bayesian nonlinear regression model, i.e., the so-called Gaussian process regression model, and describe the basic theory of this model. First, in Section 2.1.1, we illustrate how the Gaussian process can be used as a prior distribution for the unknown regression function by associating the concept of the stochastic process with a random function. We then demonstrate how to implement Gaussian process regression when a covariance function is given in Section 2.1.2. Finally, we survey asymptotic results of Gaussian process regression methods, mainly in terms of consistency. Specifically, we provide basic concepts of posterior consistency in Section 2.2, and discuss several consistency results in the Gaussian process regression method in Section 2.3. In these regards, this chapter addresses some of the technical features in Gaussian process regression, in particular asymptotic properties in terms of consistency.
2.1 Gaussian process prior and posterior
