Related papers: Variance bounding Markov chains

We prove that for a random walk on the real line whose increments have zero mean and are either integer-valued or spread out (i.e. the distributions of the steps of the walk are eventually non-singular), the Markov chain of overshoots above…

In the last decades the problem of metastability has been attacked on rigorous grounds via many different approaches and techniques which are briefly reviewed in this paper. It is then useful to understand connections between different…

We study two types of Metropolis-Hastings (MH) reversiblizations for non-reversible Markov chains with Markov kernel $P$. While the first type is the classical Metropolised version of $P$, we introduce a new self-adjoint kernel which…

The aim of this note is to investigate the concentration properties of unbounded functions of geometrically ergodic Markov chains. We derive concentration properties of centered functions with respect to the square of the Lyapunov's…

This paper surveys various results about Markov chains on general (non-countable) state spaces. It begins with an introduction to Markov chain Monte Carlo (MCMC) algorithms, which provide the motivation and context for the theory which…

A lumping of a Markov chain is a coordinate-wise projection of the chain. We characterise the entropy rate preservation of a lumping of an aperiodic and irreducible Markov chain on a finite state space by the random growth rate of the…

We consider the problem of testing the identity of a reversible Markov chain against a reference from a single trajectory of observations. Employing the recently introduced notion of a lumping-congruent Markov embedding, we show that, at…

It is shown that a seemingly harmless reordering of the steps in a block Gibbs sampler can actually invalidate the algorithm. In particular, the Markov chain that is simulated by the "out-of-order" block Gibbs sampler does not have the…

We consider a Metropolis--Hastings method with proposal $\mathcal{N}(x, hG(x)^{-1})$, where $x$ is the current state, and study its ergodicity properties. We show that suitable choices of $G(x)$ can change these compared to the Random Walk…

We study the algorithmic robustness of general finite Markov chains in terms of their stationary distributions to general, adversarial corruptions of the transition matrix. We show that for Markov chains admitting a spectral gap, variants…

We argue that the spectral theory of non-reversible Markov chains may often be more effectively cast within the framework of the naturally associated weighted-$L_\infty$ space $L_\infty^V$, instead of the usual Hilbert space $L_2=L_2(\pi)$,…

We prove an invariance principle for non-stationary random processes and establish a rate of convergence under a new type of mixing condition. The dependence is exponentially decaying in the gap between the past and the future and is…

In this paper we discuss how the notion of subgeometric ergodicity in Markov chain theory can be exploited to study stationarity and ergodicity of nonlinear time series models. Subgeometric ergodicity means that the transition probability…

We develop a theory of weak Poincar\'e inequalities to characterize convergence rates of ergodic Markov chains. Motivated by the application of Markov chains in the context of algorithms, we develop a relevant set of tools which enable the…

We investigate the use of a certain class of functional inequalities known as weak Poincar\'e inequalities to bound convergence of Markov chains to equilibrium. We show that this enables the straightforward and transparent derivation of…

This paper deals with the ergodicity and the existence of a strong law of large numbers for adaptive Markov Chain Monte Carlo. We show that a diminishing adaptation assumption together with a drift condition for positive recurrence is…

In this paper, we establish moment and Bernstein-type inequalities for additive functionals of geometrically ergodic Markov chains. These inequalities extend the corresponding inequalities for independent random variables. Our conditions…

We propose a random adaptation variant of time-varying distributed averaging dynamics in discrete time. We show that this leads to novel interpretations of fundamental concepts in distributed averaging, opinion dynamics, and distributed…

We prove an upper bound on the total variation mixing time of a finite Markov chain in terms of the absolute spectral gap and the number of elements in the state space. Unlike results requiring reversibility or irreducibility, this bound is…

This paper proposes a new type of recurrence where we divide the Markov chains into intervals that start when the chain enters into a subset A, then sample another subset B far away from A and end when the chain again return to A. The…