Grapham User Guide

where f is a function of interest on the space X, which is typically R, but can also have integer-valued components. The term “graphical model” in this setting simply means that the target density π, or the“model,” is determined by a collection of conditional probability densities. For example, suppose X = R, and that the density π is given as π(x1, x2, x3) = cp1(x1)p2(x2 | x1)p3(x3 | x1). That is, p1 determines a probability density in R, and p1( · | x) and p2( · | x) are conditional probability densities, i.e. specify a probability density for each x ∈ R. Figure 1 illustrates this model. The reader unfamiliar with graphical models is advised to take a look at some introductory material, e.g. [11, 12].