Related papers: Non-coupling from the past

A Markov chain $X^i$ on a finite state space $S$ has transition matrix $P$ and initial state $i$. We may run the chains $(X^i: i\in S)$ in parallel, while insisting that any two such chains coalesce whenever they are simultaneously at the…

We present a novel approach to quantizing Markov chains. The approach is based on the Markov chain coupling method, which is frequently used to prove fast mixing. Given a particular coupling, e.g., a grand coupling, we construct a…

I show how to run an N-time-step Markov chain simulation in a circular fashion, so that the state at time 0 follows the state at time N-1 in the same way as states at times t follow those at times t-1 for 0<t<N. This wrap-around of the…

Perfect sampling is a technique that uses coupling arguments to provide a sample from the stationary distribution of a Markov chain in a finite time without ever computing the distribution. This technique is very efficient if all the events…

We use coupling to study the time taken until the distribution of a statistic on a Markov chain is close to its stationary distribution. Coupling is a common technique used to obtain upper bounds on mixing times of Markov chains, and we…

The notion of a successful coupling of Markov processes, based on the idea that both components of the coupled system ``intersect'' in finite time with probability one, is extended to cover situations when the coupling is unnecessarily…

We introduce the idea that resampling from past observations in a Markov Chain Monte Carlo sampler can fasten convergence. We prove that proper resampling from the past does not disturb the limit distribution of the algorithm. We illustrate…

This simple note lays out a few observations which are well known in many ways but may not have been said in quite this way before. The basic idea is that when comparing two different Markov chains it is useful to couple them is such a way…

We give a new method for generating perfectly random samples from the stationary distribution of a Markov chain. The method is related to coupling from the past (CFTP), but only runs the Markov chain forwards in time, and never restarts it…

Consider a continuous-state branching population constructed as a flow of nested subordinators. Inverting the subordinators and reversing time give rise to a flow of coalescing Markov processes (with negative jumps) which correspond to the…

We apply coupling techniques in order to prove that the transfer operators associated with random topological Markov chains and non-stationary shift spaces with the big images and preimages-property have a spectral gap.

In this paper we develop a general framework for constructing and analysing coupled Markov chain Monte Carlo samplers, allowing for both (possibly degenerate) diffusion and piecewise deterministic Markov processes. For many performance…

We survey existing techniques to bound the mixing time of Markov chains. The mixing time is related to a geometric parameter called conductance which is a measure of edge-expansion. Bounds on conductance are typically obtained by a…

In this article we extend the coupling method from classical probability theory to quantum Markov chains on atomic von Neumann algebras. In particular, we establish a coupling inequality, which allow us to estimate convergence rates by…

In this paper, we study consistent and partially exchangeable sequences of Markov chains on a finite state space. We provide a characterisation of the admissible transition rates via a decomposition into individual and coordinated motion of…

Thermalization is one of the most important phenomena in statistical physics. Often, the transition probabilities between different states in the phase space is or can be approximated by constants. In this case, the system can be described…

We show that Markov couplings can be used to improve the accuracy of Markov chain Monte Carlo calculations in some situations where the steady-state probability distribution is not explicitly known. The technique generalizes the notion of…

In this work, we study how to efficiently obtain perfect samples from a discrete distribution $\mathcal{D}$ given access only to pairwise comparisons of elements of its support. Specifically, we assume access to samples $(x, S)$, where $S$…

We apply the recently proposed quantum probing protocols with an unknown system-probe coupling to probe the convex coefficients in mixtures of commuting states. By using two reference states instead of one as originally suggested, we are…

This review paper provides an introduction of Markov chains and their convergence rates which is an important and interesting mathematical topic which also has important applications for very widely used Markov chain Monte Carlo (MCMC)…