Bayesian inversion techniques for stochastic partial differential equations

DOI10.3934/jimo.2023051OpenAlexW4382488148MaRDI QIDQ6059574

Alexandros M. Pasiouras, Athanasios N. Yannacopoulos, Apostolos N. Burnetas

Publication date: 2 November 2023

Published in: Journal of Industrial and Management Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/jimo.2023051

zbMATH Keywords

inverse problemsGaussian noiseBayesian regularizationinitial condition recovery

Mathematics Subject Classification ID

Numerical methods (including Monte Carlo methods) (91G60) Bayesian problems; characterization of Bayes procedures (62C10) Interest rates, asset pricing, etc. (stochastic models) (91G30) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solution to inverse problems in abstract spaces (65J22) Regularization by noise (60H50)

Cites Work

• CMARS: a new contribution to nonparametric regression with multivariate adaptive regression splines supported by continuous optimization
• A simplified Tikhonov regularization method for determining the heat source
• A new Tikhonov regularization method
• Hyperpriors for Matérn fields with applications in Bayesian inversion
• Martingale methods in financial modelling.
• A numerical technique for solving IHCPs using Tikhonov regularization method
• Statistical and computational inverse problems.
• Bayesian posterior contraction rates for linear severely ill-posed inverse problems
• Parameter estimation for SPDEs based on discrete observations in time and space
• Bayesian linear inverse problems in regularity scales
• Discretization-invariant Bayesian inversion and Besov space priors
• On infinite-dimensional hierarchical probability models in statistical inverse problems
• Sylvester Tikhonov-regularization methods in image restoration
• Interest rate models: an infinite dimensional stochastic analysis perspective
• Transformations of Wiener integrals under translations
• Statistical Regularization of Inverse Problems
• MODELING TERM STRUCTURE DYNAMICS: AN INFINITE DIMENSIONAL APPROACH
• Approximation of Bayesian Inverse Problems for PDEs
• Maximuma posterioriprobability estimates in infinite-dimensional Bayesian inverse problems
• The estimation of residual variance in nonparametric regression
• Bayesian analysis in inverse problems
• Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation
• Tikhonov Regularization and Total Least Squares
• Sparsity in Bayesian inversion of parametric operator equations
• New approaches to regression by generalized additive models and continuous optimization for modern applications in finance, science and technology
• Data assimilation: Mathematical and statistical perspectives
• Unnamed Item
• Unnamed Item
• Unnamed Item