Exact Sampling from a Continuous State Space

Abstract

Propp & Wilson (1996) described a protocol, called coupling from the past, for exact sampling from a target distribution using a coupled Markov chain Monte Carlo algorithm. In this paper we extend coupling from the past to various MCMC samplers on a continuous state space; rather than following the monotone sampling device of Propp & Wilson, our approach uses methods related to gamma-coupling and rejection sampling to simulate the chain, and direct accounting of sample paths.

Some of Statistics Canada’s Contributions to Survey Methodology

“…In some cases, even running the algorithm for months on the world's fastest computers would not provide a remotely reasonable approximation to π. Overcoming such problems has often necessitated new and more complicated MCMC algorithms; see, e.g., Bélisle et al (1993), Neal (2003), Jain and Neal (2004), and Hamze and de Freitas (2012). In a different direction, detecting convergence of MCMC to π is so challenging that some authors have developed perfect sampling algorithms which guarantee complete convergence at the expense of a more complicated algorithm; see, e.g., Propp and Wilson (1996), Murdoch and Green (1998) or Fill et al (2000). However, such perfect sampling algorithms are often infeasible to run, so we do not discuss them further here.…”

A New Method for Coupling Random Fields

“…The bounds (8) are not needed to implement the simple field coupler. If they are available, however, we can obtain an estimate of the speed of convergence to a finitely coupled field within > 0.…”

“…Note that we have not assumed that q(·) is symmetric. For symmetric and unimodal increment distributions, an alternative field coupling method for X exists, proposed by Murdoch and Green [8]. Their method, called the bisection coupler, uses translations and reflections to construct a finitely coupled field, and appears to require fewer computations in general.…”

Perfectly random sampling of truncated multinormal distributions

“…The difficulty is that unless the dynamic is monotone, it is necessary to effectively couple all (noncountable) initial states. Murdoch and Green (1998) proposed various procedures to transform the infinite set of initial states into a more tractable finite subset.…”