Solving Geophysical Inversion Problems with Intractable Likelihoods: Linearized Gaussian Approximations Versus the Correlated Pseudo-marginal Method

Abstract A geophysical Bayesian inversion problem may target the posterior distribution of geological or hydrogeological parameters given data. To account for scatter in petrophysical relationship linking to properties, this study treats intermediate properties as latent (unobservable) variables. perform such a variable model, intractable likelihood function (hydro)geological data needs be estimated. This can achieved by approximation with Gaussian probability density based on local linearization forward operator, thereby, accounting noise corresponding addition covariance matrix. The new approximate method is compared against general correlated pseudo-marginal method, which estimates Monte Carlo averaging over samples variable. First, performances two methods are tested synthetic test example, multivariate porosity field inferred using crosshole ground-penetrating radar first-arrival travel times. For example rather small uncertainty, provide near-identical estimates, while an that ignores uncertainty leads biased estimates. results sensitivity analysis then used suggest linearized approach, attractive due its relative computational speed, suffers from decreasing accuracy increasing relationship. computationally more expensive performs very well even settings high uncertainty.