Bayesian model inversion using stochastic spectral embedding

In this paper we propose a new sampling-free approach to solve Bayesian model inversion problems that is an extension of the previously proposed spectral likelihood expansions (SLE) method. Our approach, called stochastic embedding (SSLE), uses recently presented (SSE) method for local expansion refinement approximate function at core problems. We show that, similar SLE, results in analytical expressions key statistics posterior distribution, such as evidence, moments and marginals, by direct post-processing coefficients. Because SSLE SSE rely on approximation function, they are way independent computational/mathematical complexity forward model. further enhance efficiency introducing specific adaptive sample enrichment scheme. To showcase performance SSLE, three exhibit different kinds function: multimodality, high concentration nominal dimensionality. demonstrate how significantly improves present it promising alternative existing frameworks.