Unbiased Markov chain Monte Carlo methods with couplings
By Pierre E. Jacob, John O'Leary, Yves F. Atchadé. Journal of The Royal Statistical Society Series B-statistical Methodology, 2020
147 citations recorded by the source corpus.
Markov chain Monte Carlo (MCMC) methods provide consistent approximations of integrals as the number of iterations goes to ∞. MCMC estimators are generally biased after any fixed number of iterations. We propose to remove this bias by using couplings of Markov chains together with a telescopic sum argument of Glynn and Rhee. The resulting unbiased estimators can be computed independently in parallel. We discuss practical couplings for popular MCMC algorithms. We establish the theoretical validity of the estimators proposed and study their efficiency relative to the underlying MCMC algorithms. Finally, we illustrate the performance and limitations of the method on toy examples, on an Ising model around its critical temperature, on a high dimensional variable‐selection problem, and on an approximation of the cut distribution arising in Bayesian inference for models made of multiple modules.
Subfields: Artificial Intelligence, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/cf56e5449bd9e2db35b3a6443e2e3502558359a6
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Ruben Loaiza-Maya
- Gary Koop
- Gael M. Martin
- John M. Maheu
- Anastasios Panagiotelis
- Didier Nibbering
- David T. Frazier
- Florian Huber
In Statistics and Probability
- Ruben Loaiza-Maya
- Gary Koop
- Gael M. Martin
- John M. Maheu
- Anastasios Panagiotelis
- Didier Nibbering
- David T. Frazier
- Florian Huber
Citations in the corpus
- Bayesian forecasting in economics and finance: A modern review (2022, methodology): “, 2023b) can be summarized as follows: the use of more geometric information about the target posterior, most notably the use of Hamiltonian updates (Neal, 2011b; Hoffman and Gelman, 2014); the use of better MH candidate, or proposal distributions, including those that ‘adapt’ to previous draws (Not”
- Pathfinder: Parallel quasi-Newton variational inference (2021, unknown): “In the strictest sense, it requires running the chains long enough to fully forget their initial positions, as measured, for example, by coupling (Jacob et al., 2020).”