# Peskun-Tierney ordering for Markov chain and process Monte Carlo: beyond the reversible scenario

@article{Andrieu2019PeskunTierneyOF, title={Peskun-Tierney ordering for Markov chain and process Monte Carlo: beyond the reversible scenario}, author={Christophe Andrieu and Samuel Livingstone}, journal={arXiv: Probability}, year={2019} }

Historically time-reversibility of the transitions or processes underpinning Markov chain Monte Carlo methods (MCMC) has played a key r\^ole in their development, while the self-adjointness of associated operators together with the use of classical functional analysis techniques on Hilbert spaces have led to powerful and practically successful tools to characterize and compare their performance. Similar results for algorithms relying on nonreversible Markov processes are scarce. We show that…

## 26 Citations

On the Convergence Time of Some Non-Reversible Markov Chain Monte Carlo Methods

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It is commonly admitted that non-reversible Markov chain Monte Carlo (MCMC) algorithms usually yield more accurate MCMC estimators than their reversible counterparts. In this note, we show that in…

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A novel class of non-reversible Markov chains is introduced, each chain being defined on an extended state space and having an invariant probability measure admitting π as a marginal distribution.

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Subgeometric hypocoercivity for piecewise-deterministic Markov process Monte Carlo methods

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- 2021

We extend the hypocoercivity framework for piecewise-deterministic Markov process (PDMP) Monte Carlo established in [Andrieu et. al. (2018)] to heavy-tailed target distributions, which exhibit…

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A Peskun ordering between two samplers, implying a dominance of one over the other, is known among the Markov chain Monte Carlo community for being a remarkably strong result, but it is also known…

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This paper introduces the Boomerang Sampler as a novel class of continuous-time non-reversible Markov chain Monte Carlo algorithms and demonstrates theoretically and empirically that it can out-perform existing benchmark piecewise deterministic Markov processes such as the bouncy particle sampler and the Zig-Zag.

MetFlow: A New Efficient Method for Bridging the Gap between Markov Chain Monte Carlo and Variational Inference

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A new computationally efficient method to combine Variational Inference (VI) with Markov Chain Monte Carlo (MCMC) is proposed, which is amenable to the reparametrization trick and does not rely on computationally expensive reverse kernels.

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This work introduces and studies a new family of velocity jump Markov processes directly amenable to exact simulation with the following two properties: i) trajectories converge in law when a…

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