Fitting Gaussian Process Models in Python

A common applied statistics task involves building regression models to characterize non-linear relationships between variables. When we write a function that takes continuous values as inputs, we are essentially implying an infinite vector that only returns values (indexed by the inputs) when the function is called upon to do so. To make this notion of a "distribution over functions" more concrete, let's quickly demonstrate how we obtain realizations from a Gaussian process, which result in an evaluation of a function over a set of points. We are going generate realizations sequentially, point by point, using the lovely conditioning property of mutlivariate Gaussian distributions.