Introduction to Coupling-from-the-Past using R

Abstract

The purpose of this chapter is to exemplify construction of selected coupling-from-the-past algorithms, using simple examples and discussing code which can be run in the statistical scripting language R. The simple examples are: symmetric random walk with two reflecting boundaries, a very basic continuous state-space Markov chain, the Ising model with external field, and random walk with negative drift and a reflecting boundary at the origin. In parallel with this, a discussion is given of the relationship between coupling-from-the-past algorithms on the one hand, and uniform and geometric ergodicity on the other.