Convergence Rates for Penalized Least Squares Estimators in PDE Constrained Regression Problems
From MaRDI portal
Publication:4960995
DOI10.1137/18M1236137zbMath1436.62163arXiv1809.08818OpenAlexW3011651501MaRDI QIDQ4960995
Sven Wang, Richard Nickl, Sara van de Geer
Publication date: 24 April 2020
Published in: SIAM/ASA Journal on Uncertainty Quantification (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1809.08818
Bayesian nonparametricsnonlinear inverse problemsstatistical inference for partial differential equations
Asymptotic properties of nonparametric inference (62G20) Schrödinger operator, Schrödinger equation (35J10) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21)
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Cites Work
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- Bayesian inverse problems with non-conjugate priors
- Nonparametric Bernstein-von Mises theorems in Gaussian white noise
- Bayesian inverse problems with Gaussian priors
- Efficient nonparametric Bayesian inference for \(X\)-ray transforms
- Bernstein-von Mises theorems for statistical inverse problems. I: Schrödinger equation
- Iterative regularization methods for nonlinear ill-posed problems
- Asymptotic equivalence for nonparametric regression with multivariate and random design
- Nonlinear Tikhonov regularization in Hilbert scales for inverse boundary value problems with random noise
- On the injectivity and linearization of the coefficient-to-solution mapping for elliptic boundary value problems
- Asymptotic equivalence of nonparametric regression and white noise
- Least squares estimation with complexity penalties
- Nonparametric Bayesian posterior contraction rates for scalar diffusions with high-frequency data
- Nonparametric Bayesian posterior contraction rates for discretely observed scalar diffusions
- Inverse problems: A Bayesian perspective
- Penalized estimators for non linear inverse problems
- Maximuma posterioriprobability estimates in infinite-dimensional Bayesian inverse problems
- Mathematical Foundations of Infinite-Dimensional Statistical Models
- Convergence rates for Tikhonov regularisation of non-linear ill-posed problems
- Inverse diffusion theory of photoacoustics
- An Inverse Problem for the Steady State Diffusion Equation
- Elliptic Partial Differential Equations of Second Order
- An Introduction to Banach Space Theory
- Optimal a Posteriori Parameter Choice for Tikhonov Regularization for Solving Nonlinear Ill-Posed Problems
- Tikhonov regularization of nonlinear III-posed problems in hilbert scales
- From Brownian Motion to Schrödinger’s Equation
- Tikhonov regularization anda posteriorirules for solving nonlinear ill posed problems
- Modern regularization methods for inverse problems
- Convergence Rates of General Regularization Methods for Statistical Inverse Problems and Applications
- Posterior consistency for Bayesian inverse problems through stability and regression results
- Consistency and rates of convergence of nonlinear Tikhonov regularization with random noise
- Diffusion Coefficients Estimation for Elliptic Partial Differential Equations
- MAP estimators and their consistency in Bayesian nonparametric inverse problems
