Markov chain Monte Carlo (MCMC) is an essential set of tools for estimating features of
probability distributions commonly encountered in modern applications. For MCMC …

Heuristically, a discrete-time stochastic process has the Markov property if the past and
future are independent given the present. In this introductory chapter, we give the formal …

The goal of this expository paper is to describe conditions which guarantee a central limit
theorem for functionals of general state space Markov chains. This is done with a view …

Current reporting of results based on Markov chain Monte Carlo computations could be
improved. In particular, a measure of the accuracy of the resulting estimates is rarely …

Markov chain Monte Carlo is a method of producing a correlated sample to estimate features
of a target distribution through ergodic averages. A fundamental question is when sampling …

In this paper we consider Foster–Liapounov-type drift conditions for Markov chains which
imply polynomial rate convergence to stationarity in appropriate V-norms. We also show …

We present a new drift condition which implies rates of convergence to the stationary
distribution of the iterates of a ψ-irreducible aperiodic and positive recurrent transition …

The Monte Carlo expectation maximization (MCEM) algorithm is a versatile tool for inference
in incomplete data models, especially when used in combination with Markov chain Monte …

We provide a condition in terms of a supermartingale property for a functional of the Markov
process, which implies (a) f-ergodicity of strong Markov processes at a subgeometric rate …

We prove the following probabilistic properties of a multidimensional Ornstein-Uhlenbeck
process driven by a general Lévy process, under mild regularity conditions: the strong Feller …