Year: 2015
Type: article
Abstract: We consider Bayesian linear inverse problems in infinite-dimensional separable Hilbert spaces, with a Gaussian prior measure and additive Gaussian noise model, and provide an extension of the concept of Bayesian D-optimality to the infinite-dimensional case. To this end, we derive the infinite-dimensional version of the expression for the Kullback–Leibler divergence from the posterior measure to the prior measure, which is subsequently used to derive the expression for the expected information gain. We also study the notion of Bayesian A-optimality in the infinite-dimensional setting, and extend the well known (in the finite-dimensional case) equivalence of the Bayes risk of the MAP estimator with the trace of the posterior covariance, for the Gaussian linear case, to the infinite-dimensional Hilbert space case.
Source: Bayesian Analysis
DOI: 10.1214/15-ba969
Language: English
Field: Decision Sciences
Domain: Social Sciences
Open Access status: diamond
Awards: G1443680599, G1523888516, EXTREME-SCALE BAYESIAN INFERENCE FOR UNCERTAINTY QUANTIFICATION OF COMPLEX SIMULATIONS, DIAMOND: AN INTEGRATED MULTIFACETED APPROACH TO MATHEMATICS AT THE INTERFACES OF DATA, MODELS, AND DECISIONS, "NEW; UNCERTAINTY QUANTIFICATION FOR LARGE-SCALE ICE SHEET MODELING AND SIMULATION; PI - OMAR GHATTAS", CDI Type II/Collaborative Research: Ultra-high Resolution Dynamic Earth Models through Joint Inversion of Seismic and Geodynamic Data, G6071252945, NEW; QUANTIFICATION OF UNCERTAINTY IN EXTREME SCALE COMPUTATIONS (QUEST); PI - OMAR GHATTAS, G7830320759, G850458861, G8543603247
OpenAlex ID: W1954586129