The DOI matches its Crossref record; 13 of the 13 references it cites were found in a registry or an index.
Inverse problems: A Bayesian perspective
Abstract
The subject of inverse problems in differential equations is of enormous practical importance, and has also generated substantial mathematical and computational innovation. Typically some form of regularization is required to ameliorate ill-posed behaviour. In this article we review the Bayesian approach to regularization, developing a function space viewpoint on the subject. This approach allows for a full characterization of all possible solutions, and their relative probabilities, whilst simultaneously forcing significant modelling issues to be addressed in a clear and precise fashion. Although expensive to implement, this approach is starting to lie within the range of the available computational resources in many application areas. It also allows for the quantification of uncertainty and risk, something which is increasingly demanded by these applications. Furthermore, the approach is conceptually important for the understanding of simpler, computationally expedient approaches to inverse problems.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Equation of State Calculations by Fast Computing Machines
Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E. (1953) · The Journal of Chemical Physics · doi:10.1063/1.1699114 · Cited by 37,192
Monte Carlo sampling methods using Markov chains and their applications.
Hastings, W. K. (1970) · Biometrika · doi:10.1093/biomet/57.1.97 · Cited by 15,195
An Introduction To Compressive Sampling
Candes, E. J., & Wakin, M. B. (2008) · IEEE Signal Processing Magazine · doi:10.1109/msp.2007.914731 · Cited by 10,017
Sampling-based approaches to calculating marginal densities
Gelfand, A. E., & Smith, A. F. M. (1990) · Journal of the American Statistical Association · doi:10.1080/01621459.1990.10476213 · Cited by 6,606
Bayesian calibration of computer models
Kennedy, M. C., & O'Hagan, A. (2001) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/1467-9868.00294 · Cited by 4,222
Spline Models for Observational Data
Wahba, G. (1990) · doi:10.1137/1.9781611970128 · Cited by 4,184
Atmospheric Modeling, Data Assimilation and Predictability
Kalnay, E. (2002) · doi:10.1017/cbo9780511802270 · Cited by 3,391
Bernardo, J. M., & Smith, A. F. M. (1994) · Wiley Series in Probability and Statistics · doi:10.1002/9780470316870 · Cited by 2,178
T RANSITION P ATH S AMPLING : Throwing Ropes Over Rough Mountain Passes, in the Dark
Bolhuis, P. G., Chandler, D., Dellago, C., & Geissler, P. L. (2002) · Annual Review of Physical Chemistry · doi:10.1146/annurev.physchem.53.082301.113146 · Cited by 1,972
Probability and Random Processes.
Grimmett, G. R., & Stirzaker, D. R. (2001) · doi:10.1093/oso/9780198572237.001.0001 · Cited by 1,850
Cited by
Physics-informed machine learning
Karniadakis, G. E., Kevrekidis, I. G., Lu, L., Perdikaris, P., Wang, S., & Yang, L. (2021) · Nature Reviews Physics · doi:10.1038/s42254-021-00314-5 · Cited by 8,718
Zhang, D., Lu, L., Guo, L., & Karniadakis, G. E. (2019) · Journal of Computational Physics · doi:10.1016/j.jcp.2019.07.048 · Cited by 513
Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations
Yang, L., Zhang, D., & Karniadakis, G. E. (2020) · SIAM Journal on Scientific Computing · doi:10.1137/18m1225409 · Cited by 482
The Geography of Recent Genetic Ancestry across Europe
Ralph, P., & Coop, G. (2013) · PLoS Biology · doi:10.1371/journal.pbio.1001555 · Cited by 384
Metadata
- Authors
- Stuart, A. M.
- Venue
- Acta Numerica
- Publisher
- Cambridge University Press (CUP)
- Published
- 2010-05
- Volume
- 19
- Pages
- 451-559
- ISSN
- 0962-4929 (ISSN-L)
- 1474-0508
- OpenAlex
- W2149498546
- Cited by
- 1,791
- References
- 13
- FWCI
- 39.15
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Inverse problems: A Bayesian perspective. https://app.cochat.ai/papers/10.1017/s0962492910000061
- The paper
- Stuart, A. M. (2010). Inverse problems: A Bayesian perspective. Acta Numerica. https://doi.org/10.1017/s0962492910000061
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
