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.

References in corpus (11)

• emcee: The MCMC Hammer
• Dimension-independent likelihood-informed MCMC
• Likelihood-informed dimension reduction for nonlinear inverse problems
• Geometric MCMC for Infinite-Dimensional Inverse Problems
• Spectral gaps for a Metropolis-Hastings algorithm in infinite dimensions
• CosmoHammer: Cosmological parameter estimation with the MCMC Hammer
• On a generalization of the preconditioned Crank-Nicolson Metropolis algorithm
• Well-Posed Bayesian Geometric Inverse Problems Arising in Subsurface Flow
• Proposals which speed-up function-space MCMC
• Accelerated dimension-independent adaptive Metropolis
• MCMC for a hyperbolic Bayesian inverse problem in traffic flow modelling