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Ensemble sampler for infinite-dimensional inverse problems

Abstract

We introduce a new Markov chain Monte Carlo (MCMC) sampler for infinite-dimensional inverse problems. Our new sampler is based on the affine invariant ensemble sampler, which uses interacting walkers to adapt to the covariance structure of the target distribution. We extend this ensemble sampler for the first time to infinite-dimensional function spaces, yielding a highly efficient gradient-free MCMC algorithm. Because our new ensemble sampler does not require gradients or posterior covariance estimates, it is simple to implement and broadly applicable.

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Notes

  1. https://github.com/jeremiecoullon/functional_ensemble_sampler

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Acknowledgements

We thank Christopher Nemeth, Gideon Simpson, and Jonathan Weare for offering useful critiques. JC was supported by EPSRC grant EP/S00159X/1. RJW was supported by the National Science Foundation award DMS-1646339 and by New York University’s Dean’s Dissertation Fellowship. The High End Computing facility at Lancaster University provided computing resources.

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Correspondence to Jeremie Coullon.

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Coullon, J., Webber, R.J. Ensemble sampler for infinite-dimensional inverse problems . Stat Comput 31, 28 (2021). https://doi.org/10.1007/s11222-021-10004-y

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  • DOI: https://doi.org/10.1007/s11222-021-10004-y

Keywords

  • Bayesian inverse problems
  • Markov chain Monte Carlo
  • Infinite-dimensional inverse problems
  • Dimensionality reduction

Mathematics Subject Classification

  • 65C05
  • 35R30
  • 62F15