Particle Metropolis-adjusted Langevin algorithms

Nemeth, Christopher and Sherlock, Christopher and Fearnhead, Paul (2016) Particle Metropolis-adjusted Langevin algorithms. Biometrika, 103 (3). pp. 701-717. ISSN 0006-3444

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This paper proposes a new sampling scheme based on Langevin dynamics that is applicable within pseudo-marginal and particle Markov chain Monte Carlo algorithms. We investigate this algorithm's theoretical properties under standard asymptotics, which correspond to an increasing dimension of the parameters, $n$. Our results show that the behaviour of the algorithm depends crucially on how accurately one can estimate the gradient of the log target density. If the error in the estimate of the gradient is not sufficiently controlled as dimension increases, then asymptotically there will be no advantage over the simpler random-walk algorithm. However, if the error is sufficiently well-behaved, then the optimal scaling of this algorithm will be $O(n^{-1/6})$ compared to $O(n^{-1/2})$ for the random walk. Our theory also gives guidelines on how to tune the number of Monte Carlo samples in the likelihood estimate and the proposal step-size.

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This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Biometrika following peer review. The definitive publisher-authenticated version Christopher Nemeth, Chris Sherlock, and Paul Fearnhead Particle Metropolis-adjusted Langevin algorithms Biometrika (2016) 103 (3): 701-717 first published online August 24, 2016 doi 10.1093/biomet/asw020 is available online at:
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24 Nov 2015 10:06
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22 Nov 2022 01:28