HYPERDIFFERENTIAL SENSITIVITY ANALYSIS IN THE CONTEXT OF BAYESIAN INFERENCE APPLIED TO ICE-SHEET PROBLEMS
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Published:2024
Issue:3
Volume:14
Page:1-20
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ISSN:2152-5080
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Container-title:International Journal for Uncertainty Quantification
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language:en
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Short-container-title:Int. J. UncertaintyQuantification
Author:
Reese William,Hart Joseph,Waanders Bart van Bloemen,Perego Mauro,Jakeman John D.,Saibaba Arvind K.
Abstract
Inverse problems constrained by partial differential equations (PDEs) play a critical role in model development and calibration. In many applications, there are multiple uncertain parameters in a model which must be estimated. Although the Bayesian formulation is attractive for such problems, computational cost and high dimensionality frequently prohibit a thorough exploration of the parametric uncertainty. A common approach is to reduce the dimension by fixing some parameters (which we will call auxiliary parameters) to a best estimate and use techniques from PDE-constrained optimization to approximate properties of the Bayesian posterior distribution. For instance, the maximum a posteriori probability (MAP) and the Laplace approximation of the posterior covariance can be computed. In this article, we propose using hyperdifferential sensitivity analysis (HDSA) to assess the sensitivity of the MAP point to changes in the auxiliary parameters. We establish an interpretation of HDSA as correlations in the posterior distribution. Our proposed framework is demonstrated on the inversion of bedrock topography for the Greenland ice-sheet with uncertainties arising from the basal friction coefficient and climate forcing (ice accumulation rate).
Subject
Control and Optimization,Discrete Mathematics and Combinatorics,Modeling and Simulation,Statistics and Probability
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