Comparing Transitional Markov Chain Monte Carlo and Metropolis–Hastings Sampling for Bayesian Bathymetry Reconstruction

ABSTRACT Inference in Bayesian inverse problems frequently relies on sampling‐based methods for exploring the posterior distribution. In this paper, we compare two such methods for Bayesian bathymetry reconstruction from water‐surface elevation measurements: Metropolis–Hastings Markov chain Monte Carlo (MH‐MCMC) and transitional Markov chain Monte Carlo (TMCMC). We set up the inverse problem using the one‐dimensional shallow water equations as a forward model and solve it within a Bayesian framework employing sparsity‐ and smoothness‐promoting priors. We evaluate the two sampling methods with respect to posterior exploration, reconstruction accuracy, and computational efficiency. For a low‐dimensional parameterized bathymetry test case, TMCMC demonstrates greater robustness to suboptimal local modes than MH‐MCMC, resulting in a more reliable exploration of the posterior distribution. Although both methods provide comparable reconstruction quality, TMCMC achieves a lower normalized root‐mean‐square error (NRMSE) along with lower relative and errors. Furthermore, we highlight the speed‐up achieved by parallelizing the TMCMC algorithm.