In this recipe, we'll use a Gaussian process for regression. In the linear models section, we will see how representing prior information on the coefficients was possible using Bayesian ridge regression.
With a Gaussian process, it's about the variance and not the mean. However, with a Gaussian process, we assume the mean is 0, so it's the covariance function we'll need to specify.
The basic setup is similar to how a prior can be put on the coefficients in a typical regression problem. With a Gaussian process, a prior can be put on the functional form of the data, and it's the covariance between the data points that is used to model the data, and therefore, must fit the data.
A big advantage of Gaussian processes is that they can predict probabilistically: you can obtain confidence bounds on your predictions. Additionally...
