Cotter, Colin and Cotter, Simon and Russell, Paul (2015) Parallel Adaptive Importance Sampling. [MIMS Preprint]
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Abstract
Markov chain Monte Carlo methods are a powerful and commonly used family of numerical methods for sampling from complex probability distributions. As applications of these methods increase in size and complexity, the need for efficient methods which can exploit the parallel architectures which are prevalent in high performance computing increases. In this paper, we aim to develop a framework for scalable parallel MCMC algorithms. At each iteration, an importance sampling proposal distribution is formed using the current states of all of the chains within an ensemble. Once weighted samples have been produced from this, a state-of-the-art resampling method is then used to create an evenly weighted sample ready for the next iteration. We demonstrate that this parallel adaptive importance sampling (PAIS) method outperforms naive parallelisation of serial MCMC methods using the same number of processors, for low dimensional problems, and in fact shows better than linear improvements in convergence rates with respect to the number of processors used.
| Item Type: | MIMS Preprint |
|---|---|
| Uncontrolled Keywords: | MCMC, parallel, importance sampling, Bayesian, inverse problems. |
| Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 62 Statistics MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis |
| Depositing User: | Dr Simon L Cotter |
| Date Deposited: | 03 Sep 2015 |
| Last Modified: | 08 Nov 2017 18:18 |
| URI: | https://eprints.maths.manchester.ac.uk/id/eprint/2371 |
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