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We consider optimal experimental design (OED) for Bayesian nonlinear inverse problems governed by partial differential equations (PDEs) under model uncertainty. Specifically, we consider inverse problems in which, in addition to the inversion parameters, the governing PDEs include secondary uncertain parameters. We focus on problems with infinite-dimensional inversion and secondary parameters and present a scalable computational framework for optimal design of such problems. The proposed approach enables Bayesian inversion and OED under uncertainty within a unified framework. We build on the Bayesian approximation error (BAE) approach, to incorporate modeling uncertainties in the Bayesian inverse problem, and methods for A-optimal design of infinite-dimensional Bayesian nonlinear inverse problems. Specifically, a Gaussian approximation to the posterior at the maximuma posterioriprobability point is used to define an uncertainty aware OED objective that is tractable to evaluate and optimize. In particular, the OED objective can be computed at a cost, in the number of PDE solves, that does not grow with the dimension of the discretized inversion and secondary parameters. The OED problem is formulated as a binary bilevel PDE constrained optimization problem and a greedy algorithm, which provides a pragmatic approach, is used to find optimal designs. We demonstrate the effectiveness of the proposed approach for a model inverse problem governed by an elliptic PDE on a three-dimensional domain. Our computational results also highlight the pitfalls of ignoring modeling uncertainties in the OED and/or inference stages.
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Bayesian D‐optimal design for life testing with censoring
Abstract The assumption of normality is usually tied to the design and analysis of an experimental study. However, when dealing with lifetime testing and censoring at fixed time intervals, we can no longer assume that the outcomes will be normally distributed. This generally requires the use of optimal design techniques to construct the test plan for specific distribution of interest. Optimal designs in this situation depend on the parameters of the distribution, which are generally unknown a priori. A Bayesian approach can be used by placing a prior distribution on the parameters, thereby leading to an appropriate selection of experimental design. This, along with the model and number of predictors, can be used to derive the D‐optimal design for an allowed number of experimental runs. This paper explores using this Bayesian approach on various lifetime regression models to select appropriate D‐optimal designs in regular and irregular design regions.
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- Award ID(s):
- 2134409
- PAR ID:
- 10471399
- Publisher / Repository:
- Wiley
- Date Published:
- Journal Name:
- Quality and Reliability Engineering International
- ISSN:
- 0748-8017
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1002/qre.3228
