Zobrazeno 1 - 10
of 143
pro vyhledávání: '"Alexanderian, Alen"'
We consider robust optimal experimental design (ROED) for nonlinear Bayesian inverse problems governed by partial differential equations (PDEs). An optimal design is one that maximizes some utility quantifying the quality of the solution of an invers
Externí odkaz:
http://arxiv.org/abs/2409.09137
The formulation of Bayesian inverse problems involves choosing prior distributions; choices that seem equally reasonable may lead to significantly different conclusions. We develop a computational approach to better understand the impact of the hyper
Externí odkaz:
http://arxiv.org/abs/2310.18488
We study the sensitivity of infinite-dimensional Bayesian linear inverse problems governed by partial differential equations (PDEs) with respect to modeling uncertainties. In particular, we consider derivative-based sensitivity analysis of the inform
Externí odkaz:
http://arxiv.org/abs/2310.16906
Autor:
Alexanderian, Alen
We consider the concept of Bayes risk in the context of finite-dimensional ill-posed linear inverse problem with Gaussian prior and noise models. In this note, we rederive the following well-known result: in the present Gaussian linear setting, the B
Externí odkaz:
http://arxiv.org/abs/2301.04270
Autor:
Alexanderian, Alen
We consider finite-dimensional Bayesian linear inverse problems with Gaussian priors and additive Gaussian noise models. The goal of this note is to present a simple derivation of the well-known fact that solving the Bayesian D-optimal experimental d
Externí odkaz:
http://arxiv.org/abs/2212.11466
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 paramet
Externí odkaz:
http://arxiv.org/abs/2211.03952
We provide a new perspective on the study of parameterized optimization problems. Our approach combines methods for post-optimal sensitivity analysis and ordinary differential equations to quantify the uncertainty in the minimizer due to uncertain pa
Externí odkaz:
http://arxiv.org/abs/2209.11580
We consider hyper-differential sensitivity analysis (HDSA) of nonlinear Bayesian inverse problems governed by PDEs with infinite-dimensional parameters. In previous works, HDSA has been used to assess the sensitivity of the solution of deterministic
Externí odkaz:
http://arxiv.org/abs/2202.02219
Variance-based global sensitivity analysis (GSA) can provide a wealth of information when applied to complex models. A well-known Achilles' heel of this approach is its computational cost which often renders it unfeasible in practice. An appealing al
Externí odkaz:
http://arxiv.org/abs/2201.05586
By their very nature, rare event probabilities are expensive to compute; they are also delicate to estimate as their value strongly depends on distributional assumptions on the model parameters. Hence, understanding the sensitivity of the computed ra
Externí odkaz:
http://arxiv.org/abs/2110.13974