Linear estimators and measurable linear transformations on a Hilbert space
From MaRDI portal
Publication:4743484
DOI10.1007/BF00533743zbMath0506.60004OpenAlexW2042722852MaRDI QIDQ4743484
Publication date: 1984
Published in: Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf00533743
Wiener measureconditioningfilteringlinear estimatorsGaussian measuresBayes estimatorsmeasurable linear transformations
Estimation in multivariate analysis (62H12) Gaussian processes (60G15) Bayesian problems; characterization of Bayes procedures (62C10) Signal detection and filtering (aspects of stochastic processes) (60G35) Probability theory on linear topological spaces (60B11)
Related Items
Kriging for Hilbert-space valued random fields: the operatorial point of view ⋮ Gauss-Markov processes on Hilbert spaces ⋮ Analysis of the Ensemble and Polynomial Chaos Kalman Filters in Bayesian Inverse Problems ⋮ Regularized Posteriors in Linear Ill-Posed Inverse Problems ⋮ Posterior Contraction in Bayesian Inverse Problems Under Gaussian Priors ⋮ The Bayesian formulation of EIT: analysis and algorithms ⋮ A Strongly Convergent Numerical Scheme from Ensemble Kalman Inversion ⋮ A partial overview of the theory of statistics with functional data ⋮ Computing the best linear predictor in a Hilbert space. Applications to general ARMAH processes ⋮ Uncertainty Quantification and Experimental Design for Large-Scale Linear Inverse Problems under Gaussian Process Priors ⋮ Convergence Rates for Learning Linear Operators from Noisy Data ⋮ A Hadamard fractional total variation-Gaussian (HFTG) prior for Bayesian inverse problems ⋮ A deconvolution problem with the kernel 1/[x on the plane] ⋮ SPDE bridges with observation noise and their spatial approximation ⋮ Higher order quasi-Monte Carlo integration for Bayesian PDE inversion ⋮ Hierarchical Bayesian level set inversion ⋮ Iterative updating of model error for Bayesian inversion ⋮ Wavelet-based priors accelerate maximum-a-posteriori optimization in Bayesian inverse problems ⋮ Posterior contraction rates for the Bayesian approach to linear ill-posed inverse problems ⋮ Bayesian inverse problems with Gaussian priors ⋮ Sparsity-promoting and edge-preserving maximum a posteriori estimators in non-parametric Bayesian inverse problems ⋮ The linear conditional expectation in Hilbert space ⋮ The Ornstein-Uhlenbeck bridge and applications to Markov semigroups ⋮ A consistent estimator of the smoothing operator in the functional Hodrick–Prescott filter ⋮ Importance sampling: intrinsic dimension and computational cost ⋮ On a generalization of the preconditioned Crank-Nicolson metropolis algorithm ⋮ A functional Hodrick-Prescott filter ⋮ Nonparametric estimation of an instrumental regression: a quasi-Bayesian approach based on regularized posterior ⋮ Statistical inverse problems: discretization, model reduction and inverse crimes ⋮ Fractional-order regularization and wavelet approximation to the inverse estimation problem for random fields ⋮ Solving inverse problems using data-driven models ⋮ Best linear predictor of a \(C_{[0, 1}\)-valued functional autoregressive process] ⋮ Optimal experimental design for infinite-dimensional Bayesian inverse problems governed by PDEs: a review ⋮ On the functional Hodrick-Prescott filter with non-compact operators ⋮ Oracle-type posterior contraction rates in Bayesian inverse problems
Cites Work