Some things we've learned (about Markov chain Monte Carlo)

Abstract

This paper offers a personal review of some things we've learned about rates of convergence of Markov chains to their stationary distributions. The main topic is ways of speeding up diffusive behavior. It also points to open problems and how much more there is to do.

Published in at http://dx.doi.org/10.3150/12-BEJSP09 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (6)

• Exchangeable pairs and Poisson approximation
• Markov chain comparison
• A Coupling Argument for the Random Transposition Walk
• Mixing Times of Self-Organizing Lists and Biased Permutations
• Generating Random Vectors in (Z/pZ)^d Via an Affine Random Process
• Can extra updates delay mixing?

Cited by in corpus (9)

• On the Geometric Ergodicity of Hamiltonian Monte Carlo
• Lifted Worm Algorithm for the Ising Model
• Cutoff for Almost All Random Walks on Abelian Groups
• Cutoff for Random Walks on Upper Triangular Matrices
• Exactly scale-free scale-free networks
• Markov Chain Monte Carlo for generating ranked textual data
• Exact Convergence Rate Analysis of the Independent Metropolis-Hastings Algorithms
• An asymptotic relationship between coupling methods for stochastically modeled population processes
• Constrained Monte Carlo Markov Chains on Graphs