Perturbation Bounds for Monte Carlo within Metropolis via Restricted Approximations
arXiv:1809.09547 · doi:10.1016/j.spa.2019.06.015
Abstract
The Monte Carlo within Metropolis (MCwM) algorithm, interpreted as a perturbed Metropolis-Hastings (MH) algorithm, provides an approach for approximate sampling when the target distribution is intractable. Assuming the unperturbed Markov chain is geometrically ergodic, we show explicit estimates of the difference between the n-th step distributions of the perturbed MCwM and the unperturbed MH chains. These bounds are based on novel perturbation results for Markov chains which are of interest beyond the MCwM setting. To apply the bounds, we need to control the difference between the transition probabilities of the two chains and to verify stability of the perturbed chain.
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Cited by in corpus (9)
- On the Local Lipschitz Stability of Bayesian Inverse Problems
- Two approaches to the construction of perturbation bounds for continuous-time Markov chains
- Complexity Results for MCMC derived from Quantitative Bounds
- Approximations of Geometrically Ergodic Reversible Markov Chains
- Geometric convergence of elliptical slice sampling
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- Perturbation theory for killed Markov processes and quasi-stationary distributions
- Perturbation Analysis of Markov Chain Monte Carlo for Graphical Models
- Sampling Methods for Bayesian Inference Involving Convergent Noisy Approximations of Forward Maps