Accelerating Metropolis-within-Gibbs sampler with localized computations of differential equations

Understand

Inverse problem is ubiquitous in science and engineering, and Bayesian methodologies are often used to infer the underlying parameters.

• For high dimensional temporal-spatial models, classical Markov chain Monte Carlo (MCMC) methods are often slow to converge, and it is necessary to apply Metropolis-within-Gibbs (MwG) sampling on parameter blocks.
• However, the computation cost of each MwG iteration is typically $O(n^2)$, where $n$ is the model dimension.
• This can be too expensive in practice.