2011
DOI: 10.1016/j.physd.2010.10.003
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Irreversible Monte Carlo algorithms for efficient sampling

Abstract: Equilibrium systems evolve according to Detailed Balance (DB). This principe guided development of the Monte-Carlo sampling techniques, of which Metropolis-Hastings (MH) algorithm is the famous representative. It is also known that DB is sufficient but not necessary. We construct irreversible deformation of a given reversible algorithm capable of dramatic improvement of sampling from known distribution. Our transformation modifies transition rates keeping the structure of transitions intact. To illustrate the … Show more

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Cited by 122 publications
(200 citation statements)
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“…This can be shown experimentally in special cases Suwa and Todo (2010), Turitsyn et al (2011), Vucelja (2014), theoretically in special cases Diaconis et al (2000), Neal (2004), and in fact, also in general Sun et al (2010), Chen and Hwang (2013), with respect to asymptotic variance. See also Rey-Bellet and Spiliopoulos (2014) for improved asymptotic variance of non-reversible diffusion processes on compact manifolds.…”
Section: Introductionmentioning
confidence: 75%
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“…This can be shown experimentally in special cases Suwa and Todo (2010), Turitsyn et al (2011), Vucelja (2014), theoretically in special cases Diaconis et al (2000), Neal (2004), and in fact, also in general Sun et al (2010), Chen and Hwang (2013), with respect to asymptotic variance. See also Rey-Bellet and Spiliopoulos (2014) for improved asymptotic variance of non-reversible diffusion processes on compact manifolds.…”
Section: Introductionmentioning
confidence: 75%
“…There exist two basic approaches to the construction of non-reversible chains from reversible chains: one can 'lift' the Markov chain to a larger state space Diaconis et al (2000), Neal (2004), Turitsyn et al (2011), Vucelja (2014), or one can introduce non-reversibility without altering the state space Sun et al (2010). In continuous spaces, the hybrid or Hamiltonian Monte Carlo Horowitz (1991), Neal (2011) is closely related to the lifting approach in discrete spaces.…”
Section: Introductionmentioning
confidence: 99%
“…In this section, we construct a Markov chain for the onedimensional Ising model on a basis of skew detailed balance condition (SDBC) 4) and study time evolution of the magnetization density under SDBC.…”
Section: Irreversible Glauber Dynamicsmentioning
confidence: 99%
“…3.1 Master equation and skew detailed balance condition According to the method of Turitsyn et al, 4) we introduce another Ising spin ε = ±1 in addition to the original spin configurations. The enlarged state of the system is denoted by X := (σ, ε) ∈ {−1, +1} N +1 .…”
Section: Irreversible Glauber Dynamicsmentioning
confidence: 99%
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