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APPLIED MATHEMATICS (92 journals)

Showing 1 - 82 of 82 Journals sorted alphabetically
Advances in Applied Mathematics     Full-text available via subscription   (Followers: 12)
Advances in Applied Mathematics and Mechanics     Full-text available via subscription   (Followers: 7)
Advances in Applied Mechanics     Full-text available via subscription   (Followers: 15)
AKCE International Journal of Graphs and Combinatorics     Open Access  
American Journal of Applied Mathematics and Statistics     Open Access   (Followers: 10)
American Journal of Applied Sciences     Open Access   (Followers: 22)
American Journal of Modeling and Optimization     Open Access   (Followers: 2)
Annals of Actuarial Science     Full-text available via subscription   (Followers: 2)
Applied Mathematical Modelling     Full-text available via subscription   (Followers: 23)
Applied Mathematics and Computation     Hybrid Journal   (Followers: 31)
Applied Mathematics and Mechanics     Hybrid Journal   (Followers: 4)
Applied Mathematics and Nonlinear Sciences     Open Access   (Followers: 1)
Applied Mathematics and Physics     Open Access   (Followers: 3)
Biometrical Letters     Open Access  
British Actuarial Journal     Full-text available via subscription   (Followers: 2)
Bulletin of Mathematical Sciences and Applications     Open Access  
Communication in Biomathematical Sciences     Open Access   (Followers: 2)
Communications in Applied and Industrial Mathematics     Open Access   (Followers: 1)
Communications on Applied Mathematics and Computation     Hybrid Journal   (Followers: 1)
Differential Geometry and its Applications     Full-text available via subscription   (Followers: 4)
Discrete and Continuous Models and Applied Computational Science     Open Access  
Discrete Applied Mathematics     Hybrid Journal   (Followers: 10)
Doğuş Üniversitesi Dergisi     Open Access  
e-Journal of Analysis and Applied Mathematics     Open Access  
Engineering Mathematics Letters     Open Access   (Followers: 1)
European Actuarial Journal     Hybrid Journal  
Foundations and Trends® in Optimization     Full-text available via subscription   (Followers: 2)
Frontiers in Applied Mathematics and Statistics     Open Access   (Followers: 1)
Fundamental Journal of Mathematics and Applications     Open Access  
International Journal of Advances in Applied Mathematics and Modeling     Open Access   (Followers: 1)
International Journal of Applied Mathematics and Statistics     Full-text available via subscription   (Followers: 3)
International Journal of Computer Mathematics : Computer Systems Theory     Hybrid Journal  
International Journal of Data Mining, Modelling and Management     Hybrid Journal   (Followers: 10)
International Journal of Engineering Mathematics     Open Access   (Followers: 4)
International Journal of Fuzzy Systems     Hybrid Journal  
International Journal of Swarm Intelligence     Hybrid Journal   (Followers: 2)
International Journal of Theoretical and Mathematical Physics     Open Access   (Followers: 13)
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems     Hybrid Journal   (Followers: 3)
Journal of Advanced Mathematics and Applications     Full-text available via subscription   (Followers: 1)
Journal of Advances in Mathematics and Computer Science     Open Access  
Journal of Applied & Computational Mathematics     Open Access  
Journal of Applied Intelligent System     Open Access  
Journal of Applied Mathematics & Bioinformatics     Open Access   (Followers: 6)
Journal of Applied Mathematics and Physics     Open Access   (Followers: 9)
Journal of Computational Geometry     Open Access   (Followers: 3)
Journal of Innovative Applied Mathematics and Computational Sciences     Open Access   (Followers: 11)
Journal of Mathematical Sciences and Applications     Open Access   (Followers: 2)
Journal of Mathematics and Music: Mathematical and Computational Approaches to Music Theory, Analysis, Composition and Performance     Hybrid Journal   (Followers: 12)
Journal of Mathematics and Statistics Studies     Open Access  
Journal of Physical Mathematics     Open Access   (Followers: 2)
Journal of Symbolic Logic     Hybrid Journal   (Followers: 2)
Letters in Biomathematics     Open Access   (Followers: 1)
Mathematical and Computational Applications     Open Access   (Followers: 3)
Mathematical Models and Computer Simulations     Hybrid Journal   (Followers: 3)
Mathematics and Computers in Simulation     Hybrid Journal   (Followers: 3)
Modeling Earth Systems and Environment     Hybrid Journal   (Followers: 1)
Moscow University Computational Mathematics and Cybernetics     Hybrid Journal  
Multiscale Modeling and Simulation     Hybrid Journal   (Followers: 2)
Pacific Journal of Mathematics for Industry     Open Access  
Partial Differential Equations in Applied Mathematics     Open Access   (Followers: 2)
Ratio Mathematica     Open Access  
Results in Applied Mathematics     Open Access   (Followers: 1)
Scandinavian Actuarial Journal     Hybrid Journal   (Followers: 2)
SIAM Journal on Applied Dynamical Systems     Hybrid Journal   (Followers: 3)
SIAM Journal on Applied Mathematics     Hybrid Journal   (Followers: 11)
SIAM Journal on Computing     Hybrid Journal   (Followers: 11)
SIAM Journal on Control and Optimization     Hybrid Journal   (Followers: 18)
SIAM Journal on Discrete Mathematics     Hybrid Journal   (Followers: 8)
SIAM Journal on Financial Mathematics     Hybrid Journal   (Followers: 3)
SIAM Journal on Imaging Sciences     Hybrid Journal   (Followers: 7)
SIAM Journal on Mathematical Analysis     Hybrid Journal   (Followers: 4)
SIAM Journal on Matrix Analysis and Applications     Hybrid Journal   (Followers: 3)
SIAM Journal on Numerical Analysis     Hybrid Journal   (Followers: 7)
SIAM Journal on Optimization     Hybrid Journal   (Followers: 12)
SIAM Journal on Scientific Computing     Hybrid Journal   (Followers: 16)
SIAM Review     Hybrid Journal   (Followers: 9)
SIAM/ASA Journal on Uncertainty Quantification     Hybrid Journal   (Followers: 2)
Swarm Intelligence     Hybrid Journal   (Followers: 3)
Theory of Probability and its Applications     Hybrid Journal   (Followers: 2)
Uniform Distribution Theory     Open Access  
Universal Journal of Applied Mathematics     Open Access   (Followers: 1)
Universal Journal of Computational Mathematics     Open Access   (Followers: 3)
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SIAM/ASA Journal on Uncertainty Quantification
Journal Prestige (SJR): 0.543
Citation Impact (citeScore): 1
Number of Followers: 2  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 2166-2525
Published by Society for Industrial and Applied Mathematics Homepage  [17 journals]
  • Objective Frequentist Uncertainty Quantification for Atmospheric [math]
           Retrievals

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      Authors: Pratik Patil, Mikael Kuusela, Jonathan Hobbs
      Pages: 827 - 859
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 10, Issue 3, Page 827-859, September 2022.
      Abstract. The steadily increasing amount of atmospheric carbon dioxide ([math]) is affecting the global climate system and threatening the long-term sustainability of Earth’s ecosystem. In order to better understand the sources and sinks of [math], NASA operates the Orbiting Carbon Observatory-2 and -3 satellites to monitor [math] from space. These satellites make passive radiance measurements of the sunlight reflected off the Earth’s surface in different spectral bands, which are then inverted in an ill-posed inverse problem to obtain estimates of the atmospheric [math] concentration. In this work, we propose a new [math] retrieval method that uses known physical constraints on the state variables and direct inversion of the target functional of interest to construct well-calibrated frequentist confidence intervals based on convex programming. We compare the method with the current operational retrieval procedure, which uses prior knowledge in the form of probability distributions to regularize the problem. We demonstrate that the proposed intervals consistently achieve the desired frequentist coverage, while the operational uncertainties are poorly calibrated in a frequentist sense both at individual locations and over a spatial region in a realistic simulation experiment. We also study the influence of specific nuisance state variables on the length of the proposed intervals and identify certain key variables that can greatly reduce the final uncertainty given additional deterministic or probabilistic constraints. We then develop a principled framework to incorporate such additional information into our method.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2022-08-28T07:00:00Z
      DOI: 10.1137/20M1356403
      Issue No: Vol. 10, No. 3 (2022)
       
  • Ensemble Markov Chain Monte Carlo with Teleporting Walkers

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      Authors: Michael Lindsey, Jonathan Weare, Anna Zhang
      Pages: 860 - 885
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 10, Issue 3, Page 860-885, September 2022.
      Abstract. We introduce an ensemble Markov chain Monte Carlo approach to sampling from a probability density with known likelihood. This method upgrades an underlying Markov chain by allowing an ensemble of such chains to interact via a process in which one chain’s state is cloned as another’s is deleted. This effective teleportation of states can overcome issues of metastability in the underlying chain, as the scheme enjoys rapid mixing once the modes of the target density have been populated. We derive a mean-field limit for the evolution of the ensemble. We analyze the global and local convergence of this mean-field limit, showing asymptotic convergence independent of the spectral gap of the underlying Markov chain, and moreover we interpret the limiting evolution as a gradient flow. We explain how interaction can be applied selectively to a subset of state variables in order to maintain advantage on very high-dimensional problems. Finally, we present the application of our methodology to Bayesian hyperparameter estimation for Gaussian process regression.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2022-07-29T07:00:00Z
      DOI: 10.1137/21M1425062
      Issue No: Vol. 10, No. 3 (2022)
       
  • Continuum Covariance Propagation for Understanding Variance Loss in
           Advective Systems

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      Authors: Shay Gilpin, Tomoko Matsuo, Stephen E. Cohn
      Pages: 886 - 914
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 10, Issue 3, Page 886-914, September 2022.
      Abstract. Motivated by the spurious variance loss encountered during covariance propagation in atmospheric and other large-scale data assimilation systems, we consider the problem for state dynamics governed by the continuity and related hyperbolic partial differential equations. This loss of variance has been attributed to reduced-rank representations of the covariance matrix, as in ensemble methods for example, or else to the use of dissipative numerical methods. Through a combination of analytical work and numerical experiments, we demonstrate that significant variance loss, as well as gain, typically occurs during covariance propagation, even at full rank. The cause of this unusual behavior is a discontinuous change in the continuum covariance dynamics as correlation lengths become small, for instance in the vicinity of sharp gradients in the velocity field. This discontinuity in the covariance dynamics arises from hyperbolicity: the diagonal of the kernel of the covariance operator is a characteristic surface for advective dynamics. Our numerical experiments demonstrate that standard numerical methods for evolving the state are not adequate for propagating the covariance, because they do not capture the discontinuity in the continuum covariance dynamics as correlations lengths tend to zero. Our analytical and numerical results show that this leads to significant, spurious variance loss in certain regions and gain in others. The results suggest that developing local covariance propagation methods designed specifically to capture covariance evolution near the diagonal may prove a useful alternative to current methods of covariance propagation.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2022-08-05T07:00:00Z
      DOI: 10.1137/21M1442449
      Issue No: Vol. 10, No. 3 (2022)
       
  • Scaled Vecchia Approximation for Fast Computer-Model Emulation

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      Authors: Matthias Katzfuss, Joseph Guinness, Earl Lawrence
      Pages: 537 - 554
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 10, Issue 2, Page 537-554, June 2022.
      Abstract. Many scientific phenomena are studied using computer experiments consisting of multiple runs of a computer model while varying the input settings. Gaussian processes (GPs) are a popular tool for the analysis of computer experiments, enabling interpolation between input settings, but direct GP inference is computationally infeasible for large datasets. We adapt and extend a powerful class of GP methods from spatial statistics to enable the scalable analysis and emulation of large computer experiments. Specifically, we apply Vecchia’s ordered conditional approximation in a transformed input space, with each input scaled according to how strongly it relates to the computer-model response. The scaling is learned from the data by estimating parameters in the GP covariance function using Fisher scoring. Our methods are highly scalable, enabling estimation, joint prediction, and simulation in near-linear time in the number of model runs. In several numerical examples, our approach substantially outperformed existing methods.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2022-06-29T07:00:00Z
      DOI: 10.1137/20M1352156
      Issue No: Vol. 10, No. 2 (2022)
       
  • Generative Stochastic Modeling of Strongly Nonlinear Flows with
           Non-Gaussian Statistics

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      Authors: Hassan Arbabi, Themistoklis Sapsis
      Pages: 555 - 583
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 10, Issue 2, Page 555-583, June 2022.
      Abstract. Strongly nonlinear flows, which commonly arise in geophysical and engineering turbulence, are characterized by persistent and intermittent energy transfer between various spatial and temporal scales. These systems are difficult to model and analyze due to combination of high dimensionality and uncertainty, and there has been much interest in obtaining reduced models, in the form of stochastic closures, which can replicate their non-Gaussian statistics in many dimensions. Here, we propose a data-driven framework to model stationary chaotic dynamical systems through nonlinear transformations and a set of decoupled stochastic differential equations (SDEs). Specifically, we use optimal transport to find a transformation from the distribution of time-series data to a multiplicative reference probability measure such as the standard normal distribution. Then we find the set of decoupled SDEs that admit the reference measure as the invariant measure, and also closely match the spectrum of the transformed data. As such, this framework represents the chaotic time series as the evolution of a stochastic system observed through the lens of a nonlinear map. We demonstrate the application of this framework in the Lorenz-96 system, a 10-dimensional model of high-Reynolds cavity flow, and reanalysis climate data. These examples show that SDE models generated by this framework can reproduce the non-Gaussian statistics of systems with moderate dimensions (e.g., 10 and more) and predict super-Gaussian tails that are not readily available from little training data. These findings suggest that this class of models provides an efficient hypothesis space for learning strongly nonlinear flows from small amounts of data.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2022-06-29T07:00:00Z
      DOI: 10.1137/20M1359833
      Issue No: Vol. 10, No. 2 (2022)
       
  • Multilevel Ensemble Kalman–Bucy Filters

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      Authors: Neil K. Chada, Ajay Jasra, Fangyuan Yu
      Pages: 584 - 618
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 10, Issue 2, Page 584-618, June 2022.
      Abstract. In this article we consider the linear filtering problem in continuous time. We develop and apply multilevel Monte Carlo (MLMC) strategies for ensemble Kalman–Bucy filters (EnKBFs). These filters can be viewed as approximations of conditional McKean–Vlasov-type diffusion processes. They are also interpreted as the continuous-time analogue of the ensemble Kalman filter, which has proven to be successful due to its applicability and computational cost. We prove that an ideal version of our multilevel EnKBF can achieve a mean square error (MSE) of [math], [math], with a cost of order [math]. In order to prove this result we provide a Monte Carlo convergence and approximation bounds associated to time-discretized EnKBFs. This implies a reduction in cost compared to the (single level) EnKBF which requires a cost of [math] to achieve an MSE of [math]. We test our theory on a linear Ornstein–Uhlenbeck process, which we motivate through high-dimensional examples of order [math] and [math], where we also numerically test an alternative deterministic counterpart of the EnKBF.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2022-06-29T07:00:00Z
      DOI: 10.1137/21M1423762
      Issue No: Vol. 10, No. 2 (2022)
       
  • Gaussian Processes with Input Location Error and Applications to the
           Composite Parts Assembly Process

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      Authors: Wenjia Wang, Xiaowei Yue, Benjamin Haaland, C. F. Jeff Wu
      Pages: 619 - 650
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 10, Issue 2, Page 619-650, June 2022.
      Abstract. This paper investigates Gaussian process modeling with input location error, where the inputs are corrupted by noise. Here, the best linear unbiased predictor for two cases is considered, according to whether there is noise at the target location or not. We show that the mean squared prediction error converges to a nonzero constant if there is noise at the target location, and we provide an upper bound of the mean squared prediction error if there is no noise at the target location. We investigate the use of stochastic Kriging in the prediction of Gaussian processes with input location error and show that stochastic Kriging is a good approximation when the sample size is large. Several numerical examples are given to illustrate the results, and a case study on the assembly of composite parts is presented. Technical proofs are provided in the appendices.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2022-06-29T07:00:00Z
      DOI: 10.1137/20M1312447
      Issue No: Vol. 10, No. 2 (2022)
       
  • Extrapolated Polynomial Lattice Rule Integration in Computational
           Uncertainty Quantification

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      Authors: Josef Dick, Marcello Longo, Christoph Schwab
      Pages: 651 - 686
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 10, Issue 2, Page 651-686, June 2022.
      Abstract. We present an extension of the convergence analysis for Richardson-extrapolated polynomial lattice rules from [J. Dick, T. Goda, and T. Yoshiki, SIAM J. Numer. Anal., 57 (2019), pp. 44–69] for high-dimensional, numerical integration to classes of integrand functions with quantified smoothness and quasi–Monte Carlo (QMC) integration rules with so-called smoothness-driven, product and order dependent (SPOD) weights. We establish in particular sufficient conditions for the existence of an asymptotic expansion of the QMC integration error with respect to suitable powers of N, the number of QMC integration nodes. We derive a dimension-separated criterion for a fast component-by-component (CBC) construction algorithm for the computation of the QMC generating vector with quadratic scaling with respect to the integration dimension s. We prove that the proposed QMC integration strategies (a) are free from the curse of dimensionality, (b) afford higher-order convergence rates subject to suitable summability conditions on the QMC weights, (c) allow for certain classes of high-dimensional integrand functions a computable, asymptotically exact numerical estimate of the QMC quadrature error, with reliability and efficiency independent of the dimension of the integration domain, and (d) accommodate fast, FFT-based matrix-vector multiplication from [J. Dick, F. Y. Kuo, Q. T. Le Gia, C. Schwab, SIAM J. Sci. Comput., 37 (2015), pp. A1436–A1450] when applied to parametric operator equations. The integration methods are applicable for large classes of many-parametric integrand functions with quantified parametric smoothness. We verify all hypotheses and present numerical examples arising from the Galerkin finite-element discretization of a model linear parametric elliptic PDE illustrating (a)–(d). We verify computationally the scaling of the fast CBC construction algorithm with SPOD QMC weights and examine the extrapolation-based a posteriori numerical estimation of the QMC quadrature error. We find in examples with parameter spaces of dimension s = 10, …, 128 that the extrapolation-based, computable QMC integration error indicator has an efficiency index between 0.9 and 1.1 for a moderate number N of QMC points.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2022-06-29T07:00:00Z
      DOI: 10.1137/20M1338137
      Issue No: Vol. 10, No. 2 (2022)
       
  • Risk-Adapted Optimal Experimental Design

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      Authors: Drew P. Kouri, John D. Jakeman, J. Gabriel Huerta
      Pages: 687 - 716
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 10, Issue 2, Page 687-716, June 2022.
      Abstract. Constructing accurate statistical models of critical system responses typically requires an enormous amount of experimental data. Unfortunately, physical experimentation is often expensive and time consuming. Optimal experimental design determines the ``best" allocation of experiments with respect to a criterion that measures the ability to estimate some important aspect of an assumed statistical model. While optimal design has a vast literature, few researchers have developed design paradigms targeting tail statistics, such as quantiles. In this paper, we introduce a new optimality criterion, R-optimality, that attempts to minimize the risk associated with large prediction variances. The R-optimality criterion generalizes the classical I- and G-optimality criteria and can be tailored to the risk preferences of stakeholders. We discuss numerical methods for the case when the design is supported on a finite number of points. This happens if there are only finitely many experimental configurations or if the design space is discretized. In the latter case, we prove consistency of the approximation as the number of design points increases. We demonstrate the R-optimality criterion on various numerical examples, including the calibration of a polynomial model using least-squares and quantile regression, the calibration of the nonlinear Michaelis–Menten model, and microphone placement for direct field acoustic testing—a technique used to test engineered structures in vibration environments by subjecting them to intense acoustic pressure.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2022-06-29T07:00:00Z
      DOI: 10.1137/20M1357615
      Issue No: Vol. 10, No. 2 (2022)
       
  • Quantifying Spatio-Temporal Boundary Condition Uncertainty for the North
           American Deglaciation

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      Authors: James M. Salter, Daniel B. Williamson, Lauren J. Gregoire, Tamsin L. Edwards
      Pages: 717 - 744
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 10, Issue 2, Page 717-744, June 2022.
      Abstract. Ice sheet models are used to study the deglaciation of North America at the end of the last ice age (past 21,000 years), so that we might understand whether and how existing ice sheets may reduce or disappear under climate change. Though ice sheet models have a few parameters controlling physical behavior of the ice mass, they also require boundary conditions for climate (spatio-temporal fields of temperature and precipitation, typically on regular grids and at monthly intervals). The behavior of the ice sheet is highly sensitive to these fields, and there is relatively little data from geological records to constrain them as the land was covered with ice. We develop a methodology for generating a range of plausible boundary conditions, using a low-dimensional basis representation of the spatio-temporal input. We derive this basis by combining key patterns, extracted from a small ensemble of climate model simulations of the deglaciation, with sparse spatio-temporal observations. By jointly varying the ice sheet parameters and basis vector coefficients, we run ensembles of the Glimmer ice sheet model that simultaneously explore both climate and ice sheet model uncertainties. We use these to calibrate the ice sheet physics and boundary conditions for Glimmer by ruling out regions of the joint coefficient and parameter space via history matching. We use binary ice/no ice observations from reconstructions of past ice sheet margin position to constrain this space by introducing a novel metric for history matching to binary data.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2022-06-29T07:00:00Z
      DOI: 10.1137/21M1409135
      Issue No: Vol. 10, No. 2 (2022)
       
  • Empirical Bayesian Inference Using a Support Informed Prior

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      Authors: Jiahui Zhang, Anne Gelb, Theresa Scarnati
      Pages: 745 - 774
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 10, Issue 2, Page 745-774, June 2022.
      Abstract. This paper develops a new empirical Bayesian inference algorithm for solving a linear inverse problem given multiple measurement vectors of noisy observable data. Specifically, by exploiting the joint sparsity across the multiple measurements in the sparse domain of the underlying signal or image, we construct a new support informed prior. Several applications can be modeled using this framework, including synthetic aperture radar observations using nearby azimuth angles and parallel magnetic resonance imaging. Our numerical experiments suggest that using the support informed prior usually improves accuracy of the recovery in the form of the sampled posterior mean and reduces its uncertainty when compared to posteriors constructed using some more standard priors.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2022-06-29T07:00:00Z
      DOI: 10.1137/21M140794X
      Issue No: Vol. 10, No. 2 (2022)
       
  • Monte Carlo Methods for the Neutron Transport Equation

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      Authors: Alexander M. G. Cox, Simon C. Harris, Andreas E. Kyprianou, Minmin Wang
      Pages: 775 - 825
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 10, Issue 2, Page 775-825, June 2022.
      Abstract. This paper continues our treatment of the neutron transport equation (NTE), building on the work in [A. M. G. Cox et al., J. Stat. Phys., 176 (2019), pp. 425–455; E. Horton, A. E. Kyprianou, and D. Villemonais, Ann Appl. Probab., 30 (2020), pp. 2573–2612; and S. C. Harris, E. Horton, and A. E. Kyprianou, Ann. Appl. Probab., 30 (2020), pp. 2815–2845], which describes the density (equivalently, flux) of neutrons through inhomogeneous fissile media. Our aim is to analyze existing and novel Monte Carlo (MC) algorithms, aimed at simulating the lead eigenvalue associated with the underlying model. This quantity is of principal importance in the nuclear regulatory industry, for which the NTE must be solved on complicated inhomogeneous domains corresponding to nuclear reactor cores, irradiative hospital equipment, food irradiation equipment, and so on. We include a complexity analysis of such MC algorithms, noting that no such undertaking has previously appeared in the literature. The new MC algorithms offer a variety of advantages and disadvantages of accuracy versus cost, as well as the possibility of more convenient computational parallelization.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2022-06-30T07:00:00Z
      DOI: 10.1137/21M1390578
      Issue No: Vol. 10, No. 2 (2022)
       
 
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