This is a brief guide to the notational conventions used in this text.

Scalars, vectors, and matrices

We denote scalars by either small or capital letters α, A α. We denote column vectors by bold small letters a, ϕ. When we need a row vector we usually present this as the transpose of a column vector aT, ϕT.

We represent matrices by bold capital letters B, Φ. The ith row and jth column of matrix A is written as aij. The jth column of matrix A is written as aj. When we need to refer to the ith row of a matrix, we write this as ai • where the bullet • indicates that we are considering all possible values of the column index.

We concatenate two D × 1 column vectors horizontally as a = [b, c] to form the D × 2 matrix A. We concatenate two D × 1 column vectors vertically as a = [bT,cT]T to form the 2D × 1 vector a. Although this notation is cumbersome, it allows us to represent vertical concatenations within a single line of text.

Variables and parameters

We denote variables with Roman letters a, b. The most common examples are the observed data which is always denoted by x and the state of the world which is always denoted by w. However, other hidden or latent variables are also represented by Roman letters. We denote parameters of the model by Greek letters μ, Φ, σ2. These are distinguished from variables in that there is usually a single set of parameters that explains the relation between many sets of variables.