Gaussian Process: Theory
Richard A. Davis · Wiley StatsRef: Statistics Reference Online · 2014
Abstract The class of Gaussian processes is one of the most widely used families of stochastic processes for modeling dependent data observed over time, or space, or time and space. The popularity of such processes stems primarily from two essential properties. First, a Gaussian process is completely determined by its mean and covariance functions. This property facilitates model fitting as only the first‐ and second‐order moments of the process require specification. Second, solving the prediction problem is relatively straightforward. The best predictor of a Gaussian process at an unobserved location is a linear function of the observed values and, in many cases, these functions can be computed rather quickly using recursive formulas.