Approximation bias during marginalisation over nuisance parameters in likelihood-based Variational Inference, and its impact on Bayesian solutions

Clicks: 2
ID: 313430
2026
Free PDF
Article Quality & Performance Metrics
Overall Quality
Not rated
Combines reader engagement with the AI quality analysis. This article has not been analysed, so there is no overall score — reader engagement is measured and shown alongside.
AI Quality Assessment
Not analyzed
Readership in this journal

Ranked #63 of 219 articles by views in geophysical journal international

Most read Least read

Bar heights use a square-root scale. Only the 120 most-read articles are drawn; the journal has 219 in total.

Mint this article as an NFT
Not yet minted

Create a permanent, verifiable on-chain record of this article on the Scimatic Network. The NFT is held in your Journament account, and you can withdraw it to your own wallet at any time.

5 SUSD one-off · no wallet required
Sign in to mint
Abstract
Summary Likelihood-based Variational Inference (VI) methods have recently gained traction in various fields of geophysics as they can dramatically reduce the computational cost of estimating Bayesian posterior probability distributions of target parameter values compared with traditional approaches such as Markov chain Monte Carlo (McMC) methods. In many geophysical applications of these methods, the forward problem depends also on nuisance parameters – variables that affect the forward problem, but which are not of direct interest. However, the impact on posterior estimates of marginalising over nuisance parameters in likelihood-based VI approaches remains poorly understood in geophysics. Through analytical derivation and a low-dimensional numerical example, we demonstrate that standard implementations of likelihood-based VI methods systematically underestimate posterior uncertainty when nuisance parameters are either marginalised via integration or are fixed at their maximum likelihood estimates. This underestimation occurs because Jensen’s inequality is invoked to simplify the approximation of the marginal likelihood integral, which can bias interpretations of solutions. We further show that likelihood-free VI, in particular simulation-based inference (SBI), recovers the correct posterior distribution in our experiments while remaining more computationally efficient than McMC in low dimensional problems. Our work thus clarifies conceptual differences between likelihood-based and likelihood-free Variational Inference, and in particular the impact of the approximation invoked by Jensen’s inequality.
Reference Key
openalex_W7161234854 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Sixtine Dromigny, Xuebin Zhao, Teodora Reu, Paula Koelemeijer, Andrew Curtis
Journal geophysical journal international
Year 2026
DOI
10.1093/gji/ggag180
URL
https://doi.org/10.1093/gji/ggag180
Keywords Keywords not found

Citations

No citations found. To add a citation, contact the admin at info@scimatic.org

Comments

No comments yet. Be the first to comment on this article.