activity
20152026
most citedOn the limitations of single-step drift and minorization in Markov chain convergence analysis

4 citations · 14 across the 19 of their papers we have counts for

collaborators

19 papers

math.ST2026

A spectral gap for Metropolis-adjusted Langevin algorithm with a uniformly randomized step size

Qian Qin

Let on , where is continuously differentiable and -strongly convex with a globally -Lipschitz gradient, $0…

math.PR2026

Spectral Gap for the Binary Fixed-Margin Swap Chain

Weibo Fu, Qian Qin, Guanyang Wang

We prove an explicit spectral-gap lower bound for the lazy swap chain on binary matrices with prescribed row and column sums. This chain is a standard sampler for fixed-margin null…

math.ST2026

Solidarity of Spectral Gaps for Component-Wise Markov Chains

Youngwoo Kwon, Galin Jones, Qian Qin

Deterministic-scan and random-scan component-wise Markov chain Monte Carlo algorithms, such as Gibbs samplers and conditional Metropolis-Hastings, are popular approaches for sampli…

math.ST2025

Convergence analysis of data augmentation algorithms in Bayesian lasso models with log-concave likelihoods

Jingkai Cui, Qian Qin

We study the convergence properties of a class of data augmentation algorithms targeting posterior distributions of Bayesian lasso models with log-concave likelihoods. Leveraging i…

math.ST2024

Convergence Bounds for Monte Carlo Markov Chains

Qian Qin

This review paper, written for the second edition of the Handbook of Markov Chain Monte Carlo, provides an introduction to the study of convergence analysis for Markov chain Monte…

stat.CO2024

Multivariate strong invariance principle and uncertainty assessment for time in-homogeneous cyclic MCMC samplers

Haoxiang Li, Qian Qin

Time in-homogeneous cyclic Markov chain Monte Carlo (MCMC) samplers, including deterministic scan Gibbs samplers and Metropolis within Gibbs samplers, are extensively used for samp…

math.ST2023

Geometric ergodicity of trans-dimensional Markov chain Monte Carlo algorithms

Qian Qin

This article studies the convergence properties of trans-dimensional MCMC algorithms when the total number of models is finite. It is shown that, for reversible and some non-revers…

math.ST2023

Convergence Analysis of Data Augmentation Algorithms for Bayesian Robust Multivariate Linear Regression with Incomplete Data

Haoxiang Li, Qian Qin, Galin L. Jones

Gaussian mixtures are commonly used for modeling heavy-tailed error distributions in robust linear regression. Combining the likelihood of a multivariate robust linear regression m…

math.PR2022

Spectral Telescope: Convergence Rate Bounds for Random-Scan Gibbs Samplers Based on a Hierarchical Structure

Qian Qin, Guanyang Wang

Random-scan Gibbs samplers possess a natural hierarchical structure. The structure connects Gibbs samplers targeting higher dimensional distributions to those targeting lower dimen…

math.ST2022★ 1 cited

Analysis of two-component Gibbs samplers using the theory of two projections

Qian Qin

The theory of two projections is utilized to study two-component Gibbs samplers. Through this theory, previously intractable problems regarding the asymptotic variances of two-comp…

math.ST2020★ 1 cited

Convergence Rates of Two-Component MCMC Samplers

Qian Qin, Galin L. Jones

Component-wise MCMC algorithms, including Gibbs and conditional Metropolis-Hastings samplers, are commonly used for sampling from multivariate probability distributions. A long-sta…

math.PR2020★ 4 cited

On the limitations of single-step drift and minorization in Markov chain convergence analysis

Qian Qin, James P. Hobert

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…

math.PR2019

Geometric convergence bounds for Markov chains in Wasserstein distance based on generalized drift and contraction conditions

Qian Qin, James P. Hobert

Let denote a Markov chain on a Polish space that has a stationary distribution . This article concerns upper bounds on the Wasserstein distance between…

math.ST2018★ 1 cited

Wasserstein-based methods for convergence complexity analysis of MCMC with applications

Qian Qin, James P. Hobert

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 sugge…

math.ST2017

Convergence complexity analysis of Albert and Chib's algorithm for Bayesian probit regression

Qian Qin, James P. Hobert

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 h…

math.ST2017★ 3 cited

Estimating the spectral gap of a trace-class Markov operator

Qian Qin, James P. Hobert, Kshitij Khare

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 ev…

math.ST2016★ 1 cited

Trace-class Monte Carlo Markov Chains for Bayesian Multivariate Linear Regression with Non-Gaussian Errors

Qian Qin, James P. Hobert

Let denote the intractable posterior density that results when the likelihood from a multivariate linear regression model with errors from a scale mixture of normals is combine…

math.ST2015

On the Data Augmentation Algorithm for Bayesian Multivariate Linear Regression with Non-Gaussian Errors

Qian Qin, James P. Hobert

Let denote the intractable posterior density that results when the likelihood from a multivariate linear regression model with errors from a scale mixture of normals is combine…

math.ST2015★ 3 cited

Convergence Analysis of the Data Augmentation Algorithm for Bayesian Linear Regression with Non-Gaussian Errors

James P. Hobert, Yeun Ji Jung, Kshitij Khare +1

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 tha…