The Coupling/Minorization/Drift Approach to Markov Chain Convergence Rates

08/24/2020
by   Yu Hang Jiang, et al.
0

This review paper provides an introduction of Markov chains and their convergence rates which is an important and interesting mathematical topic which also has important applications for very widely used Markov chain Monte Carlo (MCMC) algorithm. We first discuss eigenvalue analysis for Markov chains on finite state spaces. Then, using the coupling construction, we prove two quantitative bounds based on minorization condition and drift conditions, and provide descriptive and intuitive examples to showcase how these theorems can be implemented in practice. This paper is meant to provide a general overview of the subject and spark interest in new Markov chain research areas.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
08/10/2022

Poincaré inequalities for Markov chains: a meeting with Cheeger, Lyapunov and Metropolis

We develop a theory of weak Poincaré inequalities to characterize conver...
research
10/14/2019

Drift, Minorization, and Hitting Times

The “drift-and-minorization” method, introduced and popularized in (Rose...
research
10/27/2017

A note on faithful coupling of Markov chains

One often needs to turn a coupling (X_i, Y_i)_i≥ 0 of a Markov chain int...
research
01/28/2018

Air Markov Chain Monte Carlo

We introduce a class of Adapted Increasingly Rarely Markov Chain Monte C...
research
11/30/2019

Mix and Match: Markov Chains Mixing Times for Matching in Rideshare

Rideshare platforms such as Uber and Lyft dynamically dispatch drivers t...
research
11/02/2017

Consistent estimation of the spectrum of trace class data augmentation algorithms

Markov chain Monte Carlo is widely used in a variety of scientific appli...
research
12/23/2021

Bayesian Learning: A Selective Overview

This paper presents an overview of some of the concepts of Bayesian Lear...

Please sign up or login with your details

Forgot password? Click here to reset