Note Set 2, Multivariate Probability Models:

This set of notes will cover basic concepts in multivariate probability models, i.e., probability models involving multiple random variables. We will begin by discussing the important concepts of independence and conditional independence and then look at the general framework of graphical models. We will then look at specific examples of models: for joint distributions we will look at the naive Bayes probability model and Markov models, and for joint densities we will look at the multivariate Gaussian model. Note that the ideas we discuss below are applicable equally well to both discrete-valued and continuous variables (and their combinations), but we will primarily focus on discrete-valued variables in our examples.