# Bayesian model inversion using stochastic spectral embedding

arXiv: https://arxiv.org/abs/2005.07380 · HTML: https://mlsanity.com/paper/2005.07380/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 May 2020.

## Built on by (most cited first, 6 of 6)

- [Rare event estimation using stochastic spectral embedding](https://mlsanity.com/paper/2106.05824/) (2021)
- [Uncertainty Quantification and Experimental Design for Large-Scale Linear Inverse Problems under Gaussian Process Priors](https://mlsanity.com/paper/2109.03457/) (2021)
- [Dimensionality reduction can be used as a surrogate model for high-dimensional forward uncertainty quantification](https://mlsanity.com/paper/2402.04582/) (2024)
- [Multielement polynomial chaos Kriging-based metamodelling for Bayesian inference of non-smooth systems](https://mlsanity.com/paper/2212.02250/) (2022)
- [Bayesian tomography using polynomial chaos expansion and deep generative networks](https://mlsanity.com/paper/2307.04228/) (2023)
- [Maximum a Posteriori Estimation for Linear Structural Dynamics Models Using Bayesian Optimization with Rational Polynomial Chaos Expansions](https://mlsanity.com/paper/2408.03569/) (2024)

## Abstract (arXiv)

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