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A Kernel Adaptive Metropolis-Hastings algorithm is introduced, for the purpose of sampling from a target distribution with strongly nonlinear support. The algorithm embeds the trajectory of the Markov chain into a reproducing kernel Hilbert…

In the analysis of Markov chains and processes, it is sometimes convenient to replace an unbounded state space with a "truncated" bounded state space. When such a replacement is made, one often wants to know whether the equilibrium behavior…

The extremes of a univariate Markov chain with regulary varying stationary marginal distribution and asymptotically linear behavior are known to exhibit a multiplicative random walk structure called the tail chain. In this paper, we extend…

We study infinite horizon control of continuous-time non-linear branching processes with almost sure extinction for general (positive or negative) discount. Our main goal is to study the link between infinite horizon control of these…

Couplings play a central role in the analysis of Markov chain Monte Carlo algorithms and appear increasingly often in the algorithms themselves, e.g. in convergence diagnostics, parallelization, and variance reduction techniques. Existing…

There has been a recent surge of interest in coupling methods for Markov chain Monte Carlo algorithms: they facilitate convergence quantification and unbiased estimation, while exploiting embarrassingly parallel computing capabilities.…

It has become increasingly easy nowadays to collect approximate posterior samples via fast algorithms such as variational Bayes, but concerns exist about the estimation accuracy. It is tempting to build solutions that exploit approximate…

New algorithms for computing of asymptotic expansions for stationary distributions of nonlinearly perturbed semi-Markov processes are presented. The algorithms are based on special techniques of sequential phase space reduction, which can…

We revisit the statistics of extremes and records of symmetric random walks with stochastic resetting, extending earlier studies in several directions. We put forward a diffusive scaling regime (symmetric step length distribution with…

Markov chain Monte Carlo (MCMC) methods have existed for a long time and the field is well-explored. The purpose of MCMC methods is to approximate a distribution through repeated sampling; most MCMC algorithms exhibit asymptotically optimal…

We present a Markov-chain analysis of blockwise-stochastic algorithms for solving partially block-separable optimization problems. Our main contributions to the extensive literature on these methods are statements about the Markov operators…

A new model that maps a quantum random walk described by a Hadamard operator to a particular case of a random walk is presented. The model is represented by a Markov chain with a stochastic matrix, i.e., all the transition rates are…

The distribution of reversible programs tends to a limit as their size increases. For problems with a Hamming distance fitness function the limiting distribution is binomial with an exponentially small chance (but non~zero) chance of…

We construct a new Markov chain Monte Carlo method on finite states with optimal choices of acceptance-rejection ratio functions. We prove that the constructed continuous time Markov jumping process has a global in-time convergence rate in…

We study analytically a simple random walk model on a one-dimensional lattice, where at each time step the walker resets to the maximum of the already visited positions (to the rightmost visited site) with a probability $r$, and with…

The goal of this paper is to analyze distributional Markov Decision Processes as a class of control problems in which the objective is to learn policies that steer the distribution of a cumulative reward toward a prescribed target law,…

We introduce a Metropolis-Hastings Markov chain for Boltzmann distributions of classical spin systems. It relies on approximate tensor network contractions to propose correlated collective updates at each step of the evolution. We present…

We consider an elementary model for self-organised criticality, the activated random walk on the complete graph. We introduce a discrete time Markov chain as follows. At each time step, we add an active particle at a random vertex and let…

Traditional methods for unsupervised learning of finite mixture models require to evaluate the likelihood of all components of the mixture. This becomes computationally prohibitive when the number of components is large, as it is, for…

The Metropolis algorithm is a Markov chain Monte Carlo (MCMC) algorithm used to simulate from parameter distributions of interest, such as generalized linear model parameters. The "Metropolis step" is a keystone concept that underlies…