English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

An optimal experimental set-up maximizes the value of data for statisticalinferences and predictions. The efficiency of strategies for finding optimalexperimental set-ups is particularly important for experiments that aretime-consuming or expensive to perform. For instance, in the situation when theexperiments are modeled by Partial Differential Equations (PDEs), multilevelmethods have been proven to dramatically reduce the computational complexity oftheir single-level counterparts when estimating expected values. For a settingwhere PDEs can model experiments, we propose two multilevel methods forestimating a popular design criterion known as the expected information gain insimulation-based Bayesian optimal experimental design. The expected informationgain criterion is of a nested expectation form, and only a handful ofmultilevel methods have been proposed for problems of such form. We propose aMultilevel Double Loop Monte Carlo (MLDLMC), which is a multilevel strategywith Double Loop Monte Carlo (DLMC), and a Multilevel Double Loop StochasticCollocation (MLDLSC), which performs a high-dimensional integration bydeterministic quadrature on sparse grids. For both methods, the Laplaceapproximation is used for importance sampling that significantly reduces thecomputational work of estimating inner expectations. The optimal values of themethod parameters are determined by minimizing the average computational work,subject to satisfying the desired error tolerance. The computationalefficiencies of the methods are demonstrated by estimating the expectedinformation gain for Bayesian inference of the fiber orientation in compositelaminate materials from an electrical impedance tomography experiment. MLDLSCperforms better than MLDLMC when the regularity of the quantity of interest,with respect to the additive noise and the unknown parameters, can beexploited.

Multilevel Double Loop Monte Carlo and Stochastic Collocation Methods with Importance Sampling for Bayesian Optimal Experimental Design