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Geometric convergence bounds for Markov chains in Wasserstein distance based on generalized drift and contraction conditions
Let $\{X_n\}_{n=0}^\infty$ denote an ergodic Markov chain on a general state space that has stationary distribution $\pi$. This article concerns upper bounds on the $L_1$-Wasserstein distance betweenExpand
Estimating the spectral gap of a trace-class Markov operator
The utility of a Markov chain Monte Carlo algorithm is, in large part, determined by the size of the spectral gap of the corresponding Markov operator. However, calculating (and even approximating)Expand
Wasserstein-based methods for convergence complexity analysis of MCMC with applications
Over the last 25 years, techniques based on drift and minorization (d&m) have been mainstays in the convergence analysis of MCMC algorithms. However, results presented herein suggest that d&m may beExpand
Asymptotically Stable Drift and Minorization for Markov Chains with Application to Albert and Chib's Algorithm
The use of MCMC algorithms in high dimensional Bayesian problems has become routine. This has spurred so-called convergence complexity analysis, the goal of which is to ascertain how the convergenceExpand
On the limitations of single-step drift and minorization in Markov chain convergence analysis
Over the last three decades, there has been a considerable effort within the applied probability community to develop techniques for bounding the convergence rates of general state space MarkovExpand
Convergence Analysis of MCMC Algorithms for Bayesian Multivariate Linear Regression with Non‐Gaussian Errors
When Gaussian errors are inappropriate in a multivariate linear regression setting, it is often assumed that the errors are iid from a distribution that is a scale mixture of multivariate normals.Expand
Convergence Analysis of the Data Augmentation Algorithm for Bayesian Linear Regression with Non-Gaussian Errors
Gaussian errors are sometimes inappropriate in a multivariate linear regression setting because, for example, the data contain outliers. In such situations, it is often assumed that the error densityExpand
On the Iteration Complexity Analysis of Stochastic Primal-Dual Hybrid Gradient Approach with High Probability
TLDR
In this paper, we propose a stochastic Primal-Dual Hybrid Gradient (PDHG) approach for solving a wide spectrum of regularized convex optimization problems, where the regularization term is composite with a linear function. Expand
Convergence Rates of Two-Component MCMC Samplers
Component-wise MCMC algorithms, including Gibbs and conditional Metropolis-Hastings samplers, are commonly used for sampling from multivariate probability distributions. A long-standing questionExpand
Convergence complexity analysis of Albert and Chib's algorithm for Bayesian probit regression
The use of MCMC algorithms in high dimensional Bayesian problems has become routine. This has spurred so-called convergence complexity analysis, the goal of which is to ascertain how the convergenceExpand
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