Abstract:
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We propose a novel Markov chain Monte Carlo (MCMC) approach, where candidates for the next state of the Markov chain are sequentially drawn. This sequential-proposal strategy can be applied to various existing MCMC methods, including Metropolis-Hastings algorithms and methods that use deterministic proposals such as Hamiltonian Monte Carlo (HMC) and the bouncy particle sampler. We introduce a unifying framework that defines a class of algorithms that include both the Hamiltonian Monte Carlo algorithm and the bouncy particle sampler, and explain how the sequential-proposal strategy can be combined for this class of algorithms. Using the sequential-proposal strategy, we also develop new Hamiltonian Monte Carlo methods that automatically tunes the lengths of the trajectories leading to proposals, similar to the widely used No-U-Turn sampler (NUTS). The numerical efficiencies of these new methods compare favorably to that of the NUTS. Finally, we demonstrate that the sequential-proposal strategy can enable the bouncy particle sampler to pass through regions of low target density and thus facilitate better mixing of the chain when the target is multimodal. (joint work with Yves Atchade)
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