Decomposition of Multidimensional Distributions Represented by Perfect Sequences

Abstract

In contrast to most other ways used to represent multidimensional probability distributions, which are based on graphical Markov modelling (i.e., dependence structure of distributions is represented by graphs), the described approach is rather procedural. Here, we describe a process by which a multidimensional distribution can be composed from a “generating sequence” – a sequence of low-dimensional distributions. This paper gives a brief introduction to this compositional approach and reports two new theorems that are necessary for designing computational procedures within this apparatus. The first concerns computation of marginal distributions, the other gives instructions for decomposing a multidimensional model into two lower-dimensional ones.