Statistical guarantees for Bayesian uncertainty quantification in nonlinear inverse problems with Gaussian process priors
From MaRDI portal
Publication:2073706
DOI10.1214/21-AOS2082zbMath1486.62068arXiv2007.15892OpenAlexW3046449720MaRDI QIDQ2073706
François Monard, Richard Nickl, Gabriel P. Paternain
Publication date: 7 February 2022
Published in: The Annals of Statistics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2007.15892
Bayesian inference (62F15) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21)
Related Items (8)
A Bernstein–von-Mises theorem for the Calderón problem with piecewise constant conductivities ⋮ The C∞ -isomorphism property for a class of singularly-weighted x-ray transforms ⋮ The transport Oka-Grauert principle for simple surfaces ⋮ Gaussian process regression in the flat limit ⋮ High-dimensional Bernstein-von Mises theorem for the Diaconis-Ylvisaker prior ⋮ On some information-theoretic aspects of non-linear statistical inverse problems ⋮ Nonparametric Bayesian inference for reversible multidimensional diffusions ⋮ Deep learning architectures for nonlinear operator functions and nonlinear inverse problems
Cites Work
- Unnamed Item
- Unnamed Item
- Bayesian inverse problems with non-conjugate priors
- Nonparametric Bernstein-von Mises theorems in Gaussian white noise
- Fractional Laplacians on domains, a development of Hörmander's theory of \(\mu\)-transmission pseudodifferential operators
- Spectral gaps for a Metropolis-Hastings algorithm in infinite dimensions
- Whittle-Matérn priors for Bayesian statistical inversion with applications in electrical impedance tomography
- On the Bernstein-von Mises phenomenon for nonparametric Bayes procedures
- Invariant distributions, Beurling transforms and tensor tomography in higher dimensions
- Bayesian inverse problems with Gaussian priors
- The attenuated ray transform on simple surfaces
- Efficient nonparametric Bayesian inference for \(X\)-ray transforms
- Adaptive Bernstein-von Mises theorems in Gaussian white noise
- On statistical Calderón problems
- Bernstein-von Mises theorems for statistical inverse problems. I: Schrödinger equation
- On differentiable functionals
- On non-abelian Radon transform
- A Bernstein-von Mises theorem for smooth functionals in semiparametric models
- Rates of contraction of posterior distributions based on Gaussian process priors
- Asymptotic equivalence for nonparametric regression with multivariate and random design
- Asymptotic methods in statistical decision theory
- Elliptic partial differential equations of second order
- Geometric MCMC for infinite-dimensional inverse problems
- Statistical and computational inverse problems.
- Integral geometry for tensor fields. Transl. from the Russian
- The attenuated ray transform for connections and Higgs fields
- Nonparametric statistical inference for drift vector fields of multi-dimensional diffusions
- Bayesian linear inverse problems in regularity scales
- Bernstein-von Mises theorems for statistical inverse problems. II: Compound Poisson processes
- Two dimensional compact simple Riemannian manifolds are boundary distance rigid
- Posterior contraction rates for the Bayesian approach to linear ill-posed inverse problems
- The boundary rigidity problem in the presence of a magnetic field
- Posterior consistency and convergence rates for Bayesian inversion with hypoelliptic operators
- Complexity analysis of accelerated MCMC methods for Bayesian inversion
- Inverse problems: A Bayesian perspective
- Handbook of Uncertainty Quantification
- Multi-source quantitative photoacoustic tomography in a diffusive regime
- 4. Integral geometry on manifolds with boundary and applications
- 5. Non-Abelian Radon transform and its applications
- Mathematical Foundations of Infinite-Dimensional Statistical Models
- Inverse diffusion theory of photoacoustics
- ON DETERMINATION OF A GAUGE FIELD ON ℝd FROM ITS NON-ABELIAN RADON TRANSFORM ALONG ORIENTED STRAIGHT LINES
- Asymptotic Statistics
- Statistical inversion and Monte Carlo sampling methods in electrical impedance tomography
- From Brownian Motion to Schrödinger’s Equation
- Real Analysis and Probability
- Bernstein--von Mises Theorems and Uncertainty Quantification for Linear Inverse Problems
- Convergence Rates for Penalized Least Squares Estimators in PDE Constrained Regression Problems
- Consistent Inversion of Noisy <scp>Non‐Abelian X‐Ray</scp> Transforms
- Consistency of Bayesian inference with Gaussian process priors in an elliptic inverse problem
- Functional Relations, Sharp Mapping Properties, and Regularization of the X-Ray Transform on Disks of Constant Curvature
- Fundamentals of Nonparametric Bayesian Inference
- MCMC methods for functions: modifying old algorithms to make them faster
This page was built for publication: Statistical guarantees for Bayesian uncertainty quantification in nonlinear inverse problems with Gaussian process priors
