Sequential MCMC With The Discrete Bouncy Particle Sampler

Pal, Soumyasundar; Coates, Mark

doi:10.1109/ssp.2018.8450772

Cited by 4 publications

(11 citation statements)

References 18 publications

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“…At the same time, it cannot affect the better performance of the DZZ method. Like in [31], We employ Γ to obtain the 𝑀. Γ follows the equation ( 20)…”

Section: Proposal Methodsmentioning

confidence: 99%

“…However, the block MH-within Gibbs sampling is employed as the refinement step in the traditional Composite MH Kernel and it will result in extremely low sampling rate. In order to improve the efficient, HMC and DBPS [31] is proposed as the refinement step to construct 𝑞 𝑡 ,3 (•) in the Composite MH Kernel and these methods are become one class of the most effective methods.…”

Section: Problem Statementmentioning

confidence: 99%

“…DBPS is discrete version of BPS and can be implemented without simulating inhomogeneous Poisson process. Reference [31] proposed that implementing DBPS as refinement step in the Composite MH Kernel of SMCMC framework and DBPS could further improve the acceptance ratio compared with other MCMC methods. But like BPS, DBPS still has a phenomenon called reducible.…”

Section: Introductionmentioning

confidence: 99%

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The Application of Zig-Zag Sampler in Sequential Markov Chain Monte Carlo

Han¹,

Nakamura²

2021

Preprint

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Particle filtering methods are widely applied in sequential state estimation within nonlinear non-Gaussian state space model. However, the traditional particle filtering methods suffer the weight degeneracy in the high-dimensional state space model. Currently, there are many methods to improve the performance of particle filtering in high-dimensional state space model. Among these, the more advanced method is to construct the Sequential Markov chain Monte Carlo (SMCMC) framework by implementing the Composite Metropolis-Hasting (MH) Kernel. In this paper, we proposed to discretize the Zig-Zag Sampler and apply the Zig-Zag Sampler in the refinement stage of the Composite MH Kernel within the SMCMC framework which is implemented the invertible particle flow in the joint draw stage. We evaluate the performance of proposed method through numerical experiments of the challenging complex high-dimensional filtering examples. Numerical experiments show that in highdimensional state estimation examples, the proposed method improves estimation accuracy and increases the acceptance ratio compared with state-of-the-art filtering methods.

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“…At the same time, it cannot affect the better performance of the DZZ method. Like in [31], We employ Γ to obtain the 𝑀. Γ follows the equation ( 20)…”

Section: Proposal Methodsmentioning

confidence: 99%

Section: Problem Statementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Application of Zig-Zag Sampler in Sequential Markov Chain Monte Carlo

Han¹,

Nakamura²

2021

Preprint

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“…The literature on MCMC algorithms provides numerous ways in which to construct the Markov kernels K μ n . For instance, we could use Metropolis-Hastings (MH) [6], the Metropolisadjusted Langevin algorithm, Hamiltonian Monte Carlo and hybrid kernels [31], [32], or kernels based on invertible particle flow ideas [22] or on the bouncy particle sampler [28]. As an illustration, Example 1 describes a simple independent MH kernel with a proposal distribution tailored to our setting.…”

Section: Generic Mcmc-pf Algorithmmentioning

confidence: 99%

“…An alternative to these schemes in which the particles at each time step are sampled instead according to a single Markov chain Monte Carlo (MCMC) chain was proposed early on by [6]. Over recent years, there has been a renewed interest in such ideas as there is empirical evidence that these methods can outperform standard SMC algorithms in interesting scenarios (see, e.g., [8], [15], [28] , [31], and [32] for novel applications and extensions). These methods have been termed sequential MCMC methods in the literature.…”

Section: Introductionmentioning

confidence: 99%

Limit theorems for sequential MCMC methods

2020

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Both sequential Monte Carlo (SMC) methods (a.k.a. ‘particle filters’) and sequential Markov chain Monte Carlo (sequential MCMC) methods constitute classes of algorithms which can be used to approximate expectations with respect to (a sequence of) probability distributions and their normalising constants. While SMC methods sample particles conditionally independently at each time step, sequential MCMC methods sample particles according to a Markov chain Monte Carlo (MCMC) kernel. Introduced over twenty years ago in [6], sequential MCMC methods have attracted renewed interest recently as they empirically outperform SMC methods in some applications. We establish an $\mathbb{L}_r$ -inequality (which implies a strong law of large numbers) and a central limit theorem for sequential MCMC methods and provide conditions under which errors can be controlled uniformly in time. In the context of state-space models, we also provide conditions under which sequential MCMC methods can indeed outperform standard SMC methods in terms of asymptotic variance of the corresponding Monte Carlo estimators.

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Limit theorems for sequential MCMC methods

Finke,

Doucet,

Johansen

2018

Preprint

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Sequential Monte Carlo (SMC) methods, also known as particle filters (PFs), constitute a class of algorithms used to approximate expectations with respect to a sequence of probability distributions as well as the normalising constants of those distributions. Sequential Markov chain Monte Carlo (MCMC) methods are an alternative class of techniques addressing similar problems in which particles are sampled according to an MCMC kernel rather than conditionally independently at each time step. These methods were introduced over twenty years ago by Berzuini et al. (1997). Recently, there has been a renewed interest in such algorithms as they demonstrate an empirical performance superior to that of SMC methods in some applications. We establish a strong law of large numbers and a central limit theorem for sequential MCMC methods and provide conditions under which errors can be controlled uniformly in time. In the context of state-space models, we provide conditions under which sequential MCMC methods can indeed outperform standard SMC methods in terms of asymptotic variance of the corresponding Monte Carlo estimators.

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Sequential MCMC With The Discrete Bouncy Particle Sampler

Cited by 4 publications

References 18 publications

The Application of Zig-Zag Sampler in Sequential Markov Chain Monte Carlo

The Application of Zig-Zag Sampler in Sequential Markov Chain Monte Carlo

Limit theorems for sequential MCMC methods

Limit theorems for sequential MCMC methods

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