The starting point for Gaussian process regression is a multivariate normal distribution defined over the objective function. In the case of no observed training data, this is termed the prior distribution, p X . Typically it is assumed µ X = 0 for simplicity and the kernel function is chosen based on an initial guess of the properties of the objective function. Given a set of observations, D, we can "condition" the prior to produce a new distribution (which is also Gaussian), termed the posterior distribution p X|D by forming the joint distribution