Dimension-Independent MCMC Sampling for Inverse Problems with Non-Gaussian Priors

Understand

The computational complexity of MCMC methods for the exploration of complex probability measures is a challenging and important problem.

• A challenge of particular importance arises in Bayesian inverse problems where the target distribution may be supported on an infinite dimensional space.
• In practice this involves the approximation of measures defined on sequences of spaces of increasing dimension.
• Motivated by an elliptic inverse problem with non-Gaussian prior, we study the design of proposal chains for the Metropolis-Hastings algorithm with dimension independent performance.