Chapter 3 Modeling Covariance

For this course, all of the methods we discuss have a way to model the inherent dependence in the data, directly or indirectly. Ultimately, they are modeling the covariance of pairs of random variables. Before we discuss models for a specific data type, let’s think about modeling covariance more generally.

In previous sections, we discussed a random vector, a set of random variables. These random variables could represent different quantities or characteristics. We hinted that these variables could be ordered or indexed in some way.

We will formalize that here. We focus now on a random process, a series of random variables representing the same characteristic ordered or indexed by time or space.