Modern Bayesian Experimental Design

Rainforth, Tom; Foster, Adam S.; Ivanova, Desi R; Smith, Freddie Bickford

doi:10.48550/arxiv.2302.14545

Cited by 5 publications

(6 citation statements)

References 108 publications

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“…The stability of the expected utility under approximations, such as linearization and discretization, in Bayesian OED has recently been investigated in [17]. For general reviews on the topic of Bayesian OED, we refer to [1,14,49,50].…”

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confidence: 99%

Monotonicity-based regularization for shape reconstruction in linear elasticity

Eberle

Harrach

2022

Comput Mech

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We deal with the shape reconstruction of inclusions in elastic bodies. For solving this inverse problem in practice, data fitting functionals are used. Those work better than the rigorous monotonicity methods from Eberle and Harrach (Inverse Probl 37(4):045006, 2021), but have no rigorously proven convergence theory. Therefore we show how the monotonicity methods can be converted into a regularization method for a data-fitting functional without losing the convergence properties of the monotonicity methods. This is a great advantage and a significant improvement over standard regularization techniques. In more detail, we introduce constraints on the minimization problem of the residual based on the monotonicity methods and prove the existence and uniqueness of a minimizer as well as the convergence of the method for noisy data. In addition, we compare numerical reconstructions of inclusions based on the monotonicity-based regularization with a standard approach (one-step linearization with Tikhonov-like regularization), which also shows the robustness of our method regarding noise in practice.

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confidence: 99%

Monotonicity-based regularization for shape reconstruction in linear elasticity

Eberle

Harrach

2022

Comput Mech

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“…However, rigorous study of such robustness is part of future work. For more general review on Bayesian OED, see [1,9,31,34].…”

Section: Our Contributionmentioning

confidence: 99%

Bayesian design of measurements for magnetorelaxometry imaging ^*

Helin,

Hyvönen,

Maaninen

et al. 2023

Inverse Problems

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The aim of magnetorelaxometry imaging is to determine the distribution of magnetic nanoparticles inside a subject by measuring the relaxation of the superposition magnetic field generated by the nanoparticles after they have first been aligned using an external activation magnetic field that has subsequently been switched off. This work applies techniques of Bayesian optimal experimental design to (sequentially) selecting the positions for the activation coil in order to increase the value of data and enable more accurate reconstructions in a simplified measurement setup. Both Gaussian and total variation (TV) prior models are considered for the distribution of the nanoparticles. The former allows simultaneous offline computation of optimized designs for multiple consecutive activations, while the latter introduces adaptability into the algorithm by using previously measured data in choosing the position of the next activation. The TV prior has a desirable edge-enhancing characteristic, but with the downside that the computationally attractive Gaussian form of the posterior density is lost. To overcome this challenge, the lagged diffusivity iteration is used to provide an approximate Gaussian posterior model and allow the use of the standard Bayesian A- and D-optimality criteria for the TV prior as well. Two-dimensional numerical experiments are performed on a few sample targets, with the conclusion that the optimized activation positions lead, in general, to better reconstructions than symmetric reference setups when the target distribution or region of interest are nonsymmetric in shape.

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“…These studies collectively emphasise the importance of Bayesian approaches and the necessity for balancing accuracy, cost, and environmental impact in environmental monitoring and management. Despite the evident demand, widescale adoption of BOED for complex, real-world ecosystems has remained relatively limited due to significant computational challenges, particularly in adaptive scenarios or when dealing with complex models [19,20]. River and stream ecosystems, which are crucial for both ecological habitats and economic activities, are increasingly threatened by climate change, pollution, and human activities.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Design for Sampling Anomalous Spatio-Temporal Data

Buchhorn,

Mengersen,

Santos-Fernandez

et al. 2024

Preprint

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Data collected from arrays of sensors are essential for informed decision-making in various systems. However, the presence of anomalies can compromise the accuracy and reliability of insights drawn from the collected data or information obtained via statistical analysis. This study aims to develop a robust Bayesian optimal experimental design (BOED) framework with anomaly detection methods for high-quality data collection. We introduce a general framework that involves anomaly generation, detection and error scoring when searching for an optimal design. This method is demonstrated using two comprehensive simulated case studies: the first study uses a spatial dataset, and the second uses a spatio-temporal river network dataset. As a baseline approach, we employed a commonly used prediction-based utility function based on minimising errors. Results illustrate the trade-off between predictive accuracy and anomaly detection performance for our method under various design scenarios. An optimal design robust to anomalies ensures the collection and analysis of more trustworthy data, playing a crucial role in understanding the dynamics of complex systems such as the environment, therefore enabling informed decisions in monitoring, management, and response.

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Modern Bayesian Experimental Design

Cited by 5 publications

References 108 publications

Monotonicity-based regularization for shape reconstruction in linear elasticity

Monotonicity-based regularization for shape reconstruction in linear elasticity

Bayesian design of measurements for magnetorelaxometry imaging ^*

Bayesian Design for Sampling Anomalous Spatio-Temporal Data

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Modern Bayesian Experimental Design

Cited by 5 publications

References 108 publications

Monotonicity-based regularization for shape reconstruction in linear elasticity

Monotonicity-based regularization for shape reconstruction in linear elasticity

Bayesian design of measurements for magnetorelaxometry imaging *

Bayesian Design for Sampling Anomalous Spatio-Temporal Data

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Bayesian design of measurements for magnetorelaxometry imaging ^*