Asymptotic Sampling Distribution for Polynomial Chaos Representation from Data: A Maximum Entropy and Fisher Information Approach

Polynomial chaos representation of spatio-temporal random fields from experimental measurements

“…The first approach borrows ideas from the literature of pdf estimation [12] and PC coefficient estimation [30]. This approach, which can be viewed as a supplement to our previous work [30], is based on the Rosenblatt transformation that makes use of a complete set of properly ordered conditional probability distribution functions (PDFs).…”

“…This approximation is essentially similar to the independence composite likelihood representation [29]. Further work based on the principle of maximum entropy and the Rosenblatt transformation has recently been proposed to identify the asymptotic mjpdf of the PC coefficients [30]. In that work, no assumption about the underlying Gaussian process is made, and the statistical dependencies among the dominant KL components are characterized by accurately capturing their higher order joint statistical features.…”

A data‐driven stochastic collocation approach for uncertainty quantification in MEMS

“…For example, parameters for which sufficient measurements at various spatial locations are available, can be modeled as random fields. These random fields can then be expressed in terms of random variables using KL expansion [16][17][18] or PC expansion [19][20][21]. Unfortunately, for MEMS, such detailed experimental observations regarding important design parameters such as material properties and geometrical features are not available.…”

“…This approach requires prior knowledge regarding the covariance function of the random field. PC expansion can also be used to represent random fields [19][20][21], where the coefficients of the PC modes can be determined based on the principles of maximum likelihood [20] or maximum entropy (MaxEnt) [21]. An information-theoretic framework based on the principle of maximum entropy has been used in [22], in the context of stochastic material modeling, in order to assign distributions to input parameters modeled as random variables.…”

“…One may argue that the computation of the leave-one estimators in stage 2 may be computationally expensive, as it involves repeated solution of the PDE given by Equation (21). However, since we propose to use the diffusion model to improve accuracy in situations where very limited experimental information may be available, the computational cost would not be that significant.…”