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

Abstract Markov chain Monte Carlo (MCMC) is a sampling‐based method for estimating
features of probability distributions. MCMC methods produce a serially correlated, yet …

This article shows how coupled Markov chains that meet exactly after a random number of
iterations can be used to generate unbiased estimators of the solutions of the Poisson …

Abstract Markov chain Monte Carlo (MCMC) is a commonly used method for approximating
expectations with respect to probability distributions. Uncertainty assessment for MCMC …

This paper addresses the key challenge of estimating the asymptotic covariance associated
with the Markov chain central limit theorem, which is essential for visualizing and terminating …

Strong invariance principles in Markov chain Monte Carlo are crucial to theoretically
grounded output analysis. Using the wide-sense regenerative nature of ergodic Markov …

Efficient shape-constrained inference for the autocovariance sequence from a reversible
Markov chain Page 1 The Annals of Statistics 2023, Vol. 51, No. 6, 2440–2470 https://doi.org/10.1214/23-AOS2335 …

We introduce a novel statistical measure for MCMC-mean estimation, the inter-trace
variance ${\rm trv}^{(\tau_ {rel})}({\cal M}, f) $, which depends on a Markov chain ${\cal M} …

The ever-increasing power of the personal computer has led to easy parallel
implementations of Markov chain Monte Carlo (MCMC). However, almost all work in …

Stochastic gradient descent (SGD) is an estimation tool for large data employed in machine
learning and statistics. Due to the Markovian nature of the SGD process, inference is a …