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1. Bayesian inference and uncertainty propagation using efficient fractional-order viscoelastic models for dielectric elastomers

   https://doi.org/10.1177/1045389X20969847  

   Miles, Paul R ; Pash, Graham T ; Smith, Ralph C ; Oates, William S ( March 2021 , Journal of Intelligent Material Systems and Structures)

   null (Ed.)

   Dielectric elastomers are employed for a wide variety of adaptive structures. Many of these soft elastomers exhibit significant rate-dependencies in their response. Accurately quantifying this viscoelastic behavior is non-trivial and in many cases a nonlinear modeling framework is required. Fractional-order operators have been applied to modeling viscoelastic behavior for many years, and recent research has shown fractional-order methods to be effective for nonlinear frameworks. This implementation can become computationally expensive to achieve an accurate approximation of the fractional-order derivative. Accurate estimation of the elastomer’s viscoelastic behavior to quantify parameter uncertainty motivates the use of Markov Chain Monte Carlo (MCMC) methods. Since MCMC is a sampling based method, requiring many model evaluations, efficient estimation of the fractional derivative operator is crucial. In this paper, we demonstrate the effectiveness of using quadrature techniques to approximate the Riemann–Liouville definition for fractional derivatives in the context of estimating the uncertainty of a nonlinear viscoelastic model. We also demonstrate the use of parameter subset selection techniques to isolate parameters that are identifiable in the sense that they are uniquely determined by measured data. For those identifiable parameters, we employ Bayesian inference to compute posterior distributions for parameters. Finally, we propagate parameter uncertainties through the models to compute prediction intervals for quantities of interest. 

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2. Bayesian Poroelastic Aquifer Characterization From InSAR Surface Deformation Data. 2. Quantifying the Uncertainty

   https://doi.org/10.1029/2021WR029775  

   Alghamdi, Amal ; Hesse, Marc A. ; Chen, Jingyi ; Villa, Umberto ; Ghattas, Omar ( November 2021 , Water Resources Research)

   Uncertainty quantification of groundwater (GW) aquifer parameters is critical for efficient management and sustainable extraction of GW resources. These uncertainties are introduced by the data, model, and prior information on the parameters. Here, we develop a Bayesian inversion framework that uses Interferometric Synthetic Aperture Radar (InSAR) surface deformation data to infer the laterally heterogeneous permeability of a transient linear poroelastic model of a confined GW aquifer. The Bayesian solution of this inverse problem takes the form of a posterior probability density of the permeability. Exploring this posterior using classical Markov chain Monte Carlo (MCMC) methods is computationally prohibitive due to the large dimension of the discretized permeability field and the expense of solving the poroelastic forward problem. However, in many partial differential equation (PDE)‐based Bayesian inversion problems, the data are only informative in a few directions in parameter space. For the poroelasticity problem, we prove this property theoretically for a one‐dimensional problem and demonstrate it numerically for a three‐dimensional aquifer model. We design a generalized preconditioned Crank‐Nicolson (gpCN) MCMC method that exploits this intrinsic low dimensionality by using a low‐rank‐based Laplace approximation of the posterior as a proposal, which we build scalably. The feasibility of our approach is demonstrated through a real GW aquifer test in Nevada. The inherently two‐dimensional nature of InSAR surface deformation data informs a sufficient number of modes of the permeability field to allow detection of major structures within the aquifer, significantly reducing the uncertainty in the pressure and the displacement quantities of interest.

    

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3. Photometric redshift uncertainties in weak gravitational lensing shear analysis: models and marginalization

   https://doi.org/10.1093/mnras/stac3090  

   Zhang, Tianqing ; Rau, Markus Michael ; Mandelbaum, Rachel ; Li, Xiangchong ; Moews, Ben ( November 2022 , Monthly Notices of the Royal Astronomical Society)

   Recovering credible cosmological parameter constraints in a weak lensing shear analysis requires an accurate model that can be used to marginalize over nuisance parameters describing potential sources of systematic uncertainty, such as the uncertainties on the sample redshift distribution n(z). Due to the challenge of running Markov chain Monte Carlo (MCMC) in the high-dimensional parameter spaces in which the n(z) uncertainties may be parametrized, it is common practice to simplify the n(z) parametrization or combine MCMC chains that each have a fixed n(z) resampled from the n(z) uncertainties. In this work, we propose a statistically principled Bayesian resampling approach for marginalizing over the n(z) uncertainty using multiple MCMC chains. We self-consistently compare the new method to existing ones from the literature in the context of a forecasted cosmic shear analysis for the HSC three-year shape catalogue, and find that these methods recover statistically consistent error bars for the cosmological parameter constraints for predicted HSC three-year analysis, implying that using the most computationally efficient of the approaches is appropriate. However, we find that for data sets with the constraining power of the full HSC survey data set (and, by implication, those upcoming surveys with even tighter constraints), the choice of method for marginalizing over n(z) uncertainty among the several methods from the literature may modify the 1σ uncertainties on Ωm–S8 constraints by ∼4 per cent, and a careful model selection is needed to ensure credible parameter intervals.

    

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4. Hierarchical computing for hierarchical models in ecology

   https://doi.org/10.1111/2041-210X.13513  

   McCaslin, Hanna M. ; Feuka, Abigail B. ; Hooten, Mevin B. ; O'Hara, ed., Robert B. ( November 2020 , Methods in Ecology and Evolution)

   Bayesian hierarchical models allow ecologists to account for uncertainty and make inference at multiple scales. However, hierarchical models are often computationally intensive to fit, especially with large datasets, and researchers face trade‐offs between capturing ecological complexity in statistical models and implementing these models.

   We present a recursive Bayesian computing (RB) method that can be used to fit Bayesian models efficiently in sequential MCMC stages to ease computation and streamline hierarchical inference. We also introduce transformation‐assisted RB (TARB) to create unsupervised MCMC algorithms and improve interpretability of parameters. We demonstrate TARB by fitting a hierarchical animal movement model to obtain inference about individual‐ and population‐level migratory characteristics.

   Our recursive procedure reduced computation time for fitting our hierarchical movement model by half compared to fitting the model with a single MCMC algorithm. We obtained the same inference fitting our model using TARB as we obtained fitting the model with a single algorithm.

   For complex ecological statistical models, like those for animal movement, multi‐species systems, or large spatial and temporal scales, the computational demands of fitting models with conventional computing techniques can limit model specification, thus hindering scientific discovery. Transformation‐assisted RB is one of the most accessible methods for reducing these limitations, enabling us to implement new statistical models and advance our understanding of complex ecological phenomena.

    

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5. The Kernel Interaction Trick: Fast Bayesian Discovery of Pairwise Interactions in High Dimensions

   Agrawal, Raj ; Trippe, Brian ; Huggins, Jonathan ; Broderick, Tamara ( June 2019 , Proceedings of Machine Learning Research)

   Discovering interaction effects on a response of interest is a fundamental problem faced in biology, medicine, economics, and many other scientific disciplines. In theory, Bayesian methods for discovering pairwise interactions enjoy many benefits such as coherent uncertainty quantification, the ability to incorporate background knowledge, and desirable shrinkage properties. In practice, however, Bayesian methods are often computationally intractable for even moderate- dimensional problems. Our key insight is that many hierarchical models of practical interest admit a Gaussian process representation such that rather than maintaining a posterior over all O(p^2) interactions, we need only maintain a vector of O(p) kernel hyper-parameters. This implicit representation allows us to run Markov chain Monte Carlo (MCMC) over model hyper-parameters in time and memory linear in p per iteration. We focus on sparsity-inducing models and show on datasets with a variety of covariate behaviors that our method: (1) reduces runtime by orders of magnitude over naive applications of MCMC, (2) provides lower Type I and Type II error relative to state-of-the-art LASSO-based approaches, and (3) offers improved computational scaling in high dimensions relative to existing Bayesian and LASSO-based approaches. 

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