ANALYSIS OF A NONREVERSIBLE MARKOV CHAIN SAMPLER

By Persi Diaconis, Susan P. Holmes, Radford M. Neal. 2000

338 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e11681da5be491aaf80184f2127ec7ca45d42220

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Citations in the corpus

Handbook of Markov Chain Monte Carlo: Hardcover: 619 pages Publisher: Chapman and Hall/CRC Press (first edition, May 2011) Language: English ISBN-10: 1420079417 (2012, background): “Additionally, as noted by Sisson (2005), one does not need to work only with reversible Markov chains, and nonreversible chains may offer opportunities for sampler improvement (Diaconis et al., 2000; Mira and Geyer, 2000; Neal, 2004).”
Markov chain comparison (2004, background): “Let M be the Markov chain described in Section 2 of [4].”
Gossip Algorithms (2009, background): “The non-reversible random walk constructed in [16] runs on the lifted ring graph, which is denoted G2 in Figure 4.”
Zero variance Markov chain Monte Carlo for Bayesian estimators (2010, background): “These modifications have been achieved in many different ways, for example by trying to induce negative correlation along the chain path ([6,21,13,41,12]); by trying to avoid random walk behavior via successive over-relaxation ([1,36,7]); by hybrid Monte Carlo ([16,35,10,18,27]); by exploiting non r”
Improving Asymptotic Variance of MCMC Estimators: Non-reversible Chains are Better (2004, background): “This example parallels the chain analysed by Diaconis, Holmes, and Neal (2000), with c set to zero in the definition (their equation 4.1) of their chain.”
Ergodicity of the zigzag process (2017, background): “easons that PDMPs are so promising. Firstly, PDMPs are nonreversible, and it is known that nonreversible Markov processes may oﬀer faster convergence relative to reversible Markov processes (see e.g. [7, 14, 16, 20, 22, 24, 37, 41]) Secondly, a remarkable feature of the simulation procedure of some ”
Zero Variance Differential Geometric Markov Chain Monte Carlo Algorithms (2014, methodology): “…(2003)), use of Riemann sums (Philippe and Robert (2001)) or of auxiliary variables (Swendsen andWang (1987), Mira and Tierney (2002)), exploitation of non reversible Markov chains (Diaconis et al. (2000), Geyer and Mira (2000)) and data augmentation (Dyk and Meng (2001), Solgi and Mira (2013)).”
Geometric ergodicity and the spectral gap of non-reversible Markov chains (2009, methodology): “, the analysis of the MCMC sampler in [9].”
Posterior Computation with the Gibbs Zig-Zag Sampler (2020, background): “There is evidence to show that non-reversible MCMC methods can offer drastic increased sampling efﬁciency over reversible MCMC methods (Diaconis et al., 2000; Sun et al., 2010; Chen and Hwang, 2013; Rey-Bellet and Spiliopoulos, 2015).”
Gossip Algorithms for Distributed Signal Processing (2010, methodology): “buted Averaging (LADA), a scheme that uses partial locations and Markov chain lifting to create fast gossiping algorithms. Lifting of gossip algorithms is based on the seminal work of Diaconis et al. [38] and Chen et al. [39] on lifting Markov chain samplers to accelerate convergence rates. The basi”
Chernoff and Berry-Esséen inequalities for Markov processes (2001, result): “Some recent results to include non-reversible effects have been obtained in [10] and [8].”
Geometric ergodicity of the Bouncy Particle Sampler (2018, methodology): “For instance, the persistent walk on the discrete torus introduced in [11] converges to the integrated telegraph on the continuous torus [34], while the lifted chain deﬁned in [45] for spin models converges to the Zig-zag process [4] (see also the event-chain MC with inﬁnitesimal steps in the…”