Coordinate sampler: a non-reversible Gibbs-like MCMC sampler

Wu, Changye; Robert, Christian P.

doi:10.1007/s11222-019-09913-w

Cited by 19 publications

(16 citation statements)

References 24 publications

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“…( 2018 ), Bierkens et al. ( 2019 ), Wu and Robert ( 2020 ) and Power and Goldman ( 2019 ). In practice, the algorithms iterate persistent dynamics of the state variable with jumps to its direction at random event times.…”

Section: Introductionmentioning

confidence: 99%

Spatiotemporal blocking of the bouncy particle sampler for efficient inference in state-space models

Goldman

Singh

2021

Stat Comput

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We propose a novel blocked version of the continuous-time bouncy particle sampler of Bouchard-Côté et al. (J Am Stat Assoc 113(522):855–867, 2018) which is applicable to any differentiable probability density. This alternative implementation is motivated by blocked Gibbs sampling for state-space models (Singh et al. in Biometrika 104(4):953–969, 2017) and leads to significant improvement in terms of effective sample size per second, and furthermore, allows for significant parallelization of the resulting algorithm. The new algorithms are particularly efficient for latent state inference in high-dimensional state-space models, where blocking in both space and time is necessary to avoid degeneracy of MCMC. The efficiency of our blocked bouncy particle sampler, in comparison with both the standard implementation of the bouncy particle sampler and the particle Gibbs algorithm of Andrieu et al. (J R Stat Soc Ser B Stat Methodol 72(3):269–342, 2010), is illustrated numerically for both simulated data and a challenging real-world financial dataset.

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Section: Introductionmentioning

confidence: 99%

Spatiotemporal blocking of the bouncy particle sampler for efficient inference in state-space models

Goldman

Singh

2021

Stat Comput

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“…In recent years there has been substantial interest in using continuous-time piecewise-deterministic Markov processes (PDMPs), as the basis for Markov chain Monte Carlo (MCMC) algorithms. These ideas started in the statistical physics literature [21], and have led to a number of new MCMC algorithms such as the Bouncy Particle Sampler (BPS) [7], the Zig-Zag (ZZ) Process [4] and the Coordinate Sampler (CS) [26], amongst many others. See [16] and [24] for an introduction to the area.…”

Section: Introductionmentioning

confidence: 99%

“…3. The Coordinate Sampler [26] uses {±e i } d i=1 as its velocity space, equipped with the uniform measure, where e i is the i th coordinate vector. Bounce events again happen at rate λ(x, v) = v, −∇ log π(x) + .…”

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confidence: 99%

PDMP Monte Carlo methods for piecewise-smooth densities

Chevallier¹,

Power²,

Wang³

et al. 2021

Preprint

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There has been substantial interest in developing Markov chain Monte Carlo algorithms based on piecewise-deterministic Markov processes. However existing algorithms can only be used if the target distribution of interest is differentiable everywhere. The key to adapting these algorithms so that they can sample from to densities with discontinuities is defining appropriate dynamics for the process when it hits a discontinuity. We present a simple condition for the transition of the process at a discontinuity which can be used to extend any existing sampler for smooth densities, and give specific choices for this transition which work with popular algorithms such as the Bouncy Particle Sampler, the Coordinate Sampler and the Zig-Zag Process. Our theoretical results extend and make rigorous arguments that have been presented previously, for instance constructing samplers for continuous densities restricted to a bounded domain, and we present a version of the Zig-Zag Process that can work in such a scenario. Our novel approach to deriving the invariant distribution of a piecewise-deterministic Markov process with boundaries may be of independent interest.

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“…This PDMP is a particular case of the process driven by (1): for instance in [23], the jump rate is given by λ(x, v) = (v • ∇ x U (x)) + , where U is a potential, and at each jump, the velocity is reflected according to optical laws on the level set of U it has reached. Recently, a new model have been studied: in [25], Robert and Wu introduce the coordinate sample, which is a variant of the Zig-Zag process, since the velocity does not live in {−1, +1} d but in {e i , 1 ≤ i ≤ d} the canonical base of R d . For this process, only one component of the position evolves between the jumps.…”

Section: Introductionmentioning

confidence: 99%

“…In fact, almost all of the recent study in dimension d do this for the sampling. Let us refer to [5,6,7,8,13,15,23,25], where the authors want to sample from a distribution with a density proportional to e −U , where U is a potential on R d . For a jump rate λ and a jump kernel Q well chosen (with respect to U ), the PDMP converges towards the targeted distribution.…”

Section: Introductionmentioning

confidence: 99%

Long-time behaviour of generalised Zig-Zag process

Fétique

2017

Preprint

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We study the long-time behaviour of a class of piecewise-deterministic Markov processes which are an extension of some recent works. These d-dimensional processes, d ≥ 1, can especially be used to model the motion of a bacterium in presence of a chemo-attractant, with parameters depending both on the position and the velocity of the bacterium. Using the method of Meyn and Tweedie ([21, 22]), we show that under some good assumptions on the parameters of the model, such a process converges exponentially fast towards its invariant measure. We also establish the existence of exponential moments of the invariant measure using results on semi-regenerative processes. The one-dimensional case is studied separately since complementary results can be obtained in that particular case.

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Coordinate sampler: a non-reversible Gibbs-like MCMC sampler

Cited by 19 publications

References 24 publications

Spatiotemporal blocking of the bouncy particle sampler for efficient inference in state-space models

Spatiotemporal blocking of the bouncy particle sampler for efficient inference in state-space models

PDMP Monte Carlo methods for piecewise-smooth densities

Long-time behaviour of generalised Zig-Zag process

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