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arXiv 2021年

作者： Zhang, Jiachen Crippa, Paola Genton, Marc G. Castruccio, Stefano Department of Applied and Computational Mathematics and Statistics University of Notre Dame United States Department of Civid and Environmental Engineering and Geoscience University of Notre Dame United States Statistics Program King Abdullah University of Science and Technology Saudi Arabia

The transition from non-renewable to renewable energies represents a global societal challenge, and developing a sustainable energy portfolio is an especially daunting task for developing countries where little to no information is available regarding the abundance of renewable resources such as wind. Weather model simulations are key to obtain such information when observational data are scarce and sparse over a country as large and geographically diverse as Saudi Arabia. However, output from such models is uncertain, as it depends on inputs such as the parametrization of the physical processes and the spatial resolution of the simulated domain. In such situations, a sensitivity analysis must be performed and the input may have a spatially heterogeneous influence of wind. In this work, we propose a latent Gaussian functional analysis of variance (ANOVA) model that relies on a nonstationary Gaussian Markov random field approximation of a continuous latent process. The proposed approach is able to capture the local sensitivity of Gaussian and non-Gaussian wind characteristics such as speed and threshold exceedances over a large simulation domain, and a continuous underlying process also allows us to assess the effect of different spatial resolutions. Our results indicate that (1) the non-local planetary boundary layer scheme and high spatial resolution are both instrumental in capturing wind speed and energy (especially over complex mountainous terrain), and (2) the impact of planetary boundary layer scheme and resolution on Saudi Arabia’s planned wind farms is small (at most 1.4%). Thus, our results lend support for the construction of these wind farms in the next decade. © 2021, CC BY-NC-ND.

关键词： Sensitivity analysis

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Symmetry groups and invariant solutions of plane Poiseuille flow

arXiv

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arXiv 2024年

作者： Aghor, Pratik P. Gibson, John F. School of Earth and Atmospheric Sciences Georgia Institute of Technology United States Integrated Applied Mathematics Program Department of Mathematics & Statistics University of New Hampshire United States

Equilibrium, traveling-wave, and periodic-orbit solutions of the Navier-Stokes equations provide a promising avenue for investigating the structure, dynamics, and statistics of transitional flows. Many such invariant solutions have been computed for wall-bounded shear flows, including plane Couette, plane Poiseuille, and pipe flow. However, the organization of invariant solutions is not well understood. In this paper we focus on the role of symmetries in the organization and computation of invariant solutions of plane Poiseuille *** show that enforcing symmetries while computing invariant solutions increases the efficiency of the numerical methods, and that redundancies between search spaces can be eliminated by consideration of equivalence relations between symmetry subgroups. We determine all symmetry subgroups of plane Poiseuille flow in a doubly-periodic domain up to translations by half the periodic lengths and classify the subgroups into equivalence classes, each of which represents a physically distinct set of symmetries and an associated set of physically distinct invariant *** calculate fifteen new traveling waves of plane Poiseuille flow in seven distinct symmetry groups and discuss their relevance to the dynamics of transitional turbulence. We present a few examples of subgroups with fractional shifts other than half the periodic lengths and one traveling wave solution whose symmetry involves shifts by one-third of the periodic lengths. We conclude with a discussion and some open questions about the role of symmetry in the behavior of shear flows. © 2024, CC BY.

关键词： Navier Stokes equations

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Nonstationary spatial modeling of massive global satellite data

arXiv

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arXiv 2021年

作者： Huang, Huang Blake, Lewis R. Katzfuss, Matthias Hammerling, Dorit M. Statistics Program King Abdullah University of Science and Technology Thuwal 23955-6900 Saudi Arabia Department of Applied Mathematics and Statistics Colorado School of Mines GoldenCO80401 United States Department of Statistics Texas A&M University College StationTX77843 United States

Earth-observing satellite instruments obtain a massive number of observations every day. For example, tens of millions of sea surface temperature (SST) observations on a global scale are collected daily by the Moderate Resolution Imaging Spectroradiometer (MODIS) instrument. Despite their size, such datasets are incomplete and noisy, necessitating spatial statistical inference to obtain complete, high-resolution fields with quantified uncertainties. Such inference is challenging due to the high computational cost, the nonstationary behavior of environmental processes on a global scale, and land barriers affecting the dependence of SST. In this work, we develop a multi-resolution approximation (M-RA) of a Gaussian process (GP) whose nonstationary, global covariance function is obtained using local fits. The M-RA requires domain partitioning, which can be set up application-specifically. In the SST case, we partition the domain purposefully to account for and weaken dependence across land barriers. Our M-RA implementation is tailored to distributed-memory computation in high-performance-computing environments. We analyze a MODIS SST dataset consisting of more than 43 million observations, to our knowledge the largest dataset ever analyzed using a probabilistic GP model. We show that our nonstationary model based on local fits provides substantially improved predictive performance relative to a stationary approach. © 2021, CC BY.

关键词： Atmospheric temperature

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Neural Methods for Amortized Inference

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statistics and Its Application 1000年第1期12卷 311-335页

作者： Andrew Zammit-Mangion Matthew Sainsbury-Dale Raphaël Huser 1School of Mathematics and Applied Statistics University of Wollongong Wollongong New South Wales Australia email: azm@uow.edu.au 2Statistics Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology (KAUST) Thuwal Saudi Arabia

Simulation-based methods for statistical inference have evolved dramatically over the past 50 years, keeping pace with technological advancements. The field is undergoing a new revolution as it embraces the representational capacity of neural networks, optimization libraries, and graphics processing units for learning complex mappings between data and inferential targets. The resulting tools are amortized, in the sense that, after an initial setup cost, they allow rapid inference through fast feed-forward operations. In this article we review recent progress in the context of point estimation, approximate Bayesian inference, summary-statistic construction, and likelihood approximation. We also cover software and include a simple illustration to showcase the wide array of tools available for amortized inference and the benefits they offer over Markov chain Monte Carlo methods. The article concludes with an overview of relevant topics and an outlook on future research directions.

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Virtual Array Processing for Active Radar and Sonar Sensing

Virtual Array Processing for Active Radar and Sonar Sensing

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Asilomar Conference on Signals, Systems & Computers

作者： Louis L. Scharf Ali Pezeshki Departments of Electrical and Computer Engineering and Statistics Colorado State University Fort Collins CO USA Program Applied and Computational Mathematics Princeton University Princeton NJ USA

In this paper, we describe how an active radar/sonar imaging problem may be formulated as a virtual passive sensor array processing problem. We consider an active sensing problem where it is desired to form a range-Doppler image at a slow- time rate, even though the radar/sonar can transmit pulses at a fast time rate. By transmitting pulses at the fast time rate we can estimate the second-order statistics of an ambiguity vector, calculated at a coarse resolution. As we show this ambiguity vector plays the role of an array snapshot vector in passive sensor array processing. The noise free version of this ambiguity vector acts as a signature vector or steering vector, which can be steered around in delay and Doppler at a fine resolution to produce an image. We employ a MVDR-like principle to generate high resolution delay-Doppler images.

关键词： Array signal processing Sonar Sensor arrays Radar imaging Delay Image resolution Passive radar Image sensors Sensor phenomena and characterization statistics

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Fractional Integrable Nonlinear Soliton Equations

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Physical Review Letters 2022年第18期128卷 184101-184101页

作者： Mark J. Ablowitz Joel B. Been Lincoln D. Carr Department of Applied Mathematics University of Colorado Boulder Colorado 80309 USA Department of Applied Mathematics and Statistics Colorado School of Mines Golden Colorado 80401 USA Department of Physics Colorado School of Mines Golden Colorado 80401 USA Quantum Engineering Program Colorado School of Mines Golden Colorado 80401 USA

Nonlinear integrable equations serve as a foundation for nonlinear dynamics, and fractional equations are well known in anomalous diffusion. We connect these two fields by presenting the discovery of a new class of integrable fractional nonlinear evolution equations describing dispersive transport in fractional media. These equations can be constructed from nonlinear integrable equations using a widely generalizable mathematical process utilizing completeness relations, dispersion relations, and inverse scattering transform techniques. As examples, this general method is used to characterize fractional extensions to two physically relevant, pervasive integrable nonlinear equations: the Korteweg–deVries and nonlinear Schrödinger equations. These equations are shown to predict superdispersive transport of nondissipative solitons in fractional media.

关键词： Solitons

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Survival analysis of the gamma-ray burst data

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Journal of the American Statistical Association 1994年第426期89卷 452-452页

作者： Efron, Bradley Petrosian, Vahé Professor/Chairman Statistics Department Stanford University CA 94305-4065 Professor of Health Research and Policy Department of Statistics Stanford University CA 94305-4065 Chairman of Astronomy Program and Professor of Physics and Applied Physics Departments Stanford University CA 94305-4065 We thank the SWiNE SMM and BATSE teams

Gamma-ray bursts are short but powerful pulses of electromagnetic radiation coming from space. Specially equipped satellites have observed the arrival of several hundred bursts during the past two decades. The origin of these bursts, whether from near the earth, across the galaxy, or out of the deep cosmos, has become a major question for astronomers. At the heart of this question lies a statistical puzzle relating to familiar issues in survival analysis Kaplan--Meier-type curves, data truncation, hazard rate analysis, Mantel--Haenszel statistics, and so on. Survival analysis is used here to critically examine two different models that have been proposed for the gamma-ray burst data. The analysis contradicts one of these models.

关键词： Bayesian statistics Climatic change Gaussian random fields

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A general sample size framework for developing or updating a clinical prediction model

arXiv

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arXiv 2025年

作者： Riley, Richard D. Whittle, Rebecca Sadatsafavi, Mohsen Martin, Glen P. Pate, Alexander Collins, Gary S. Ensor, Joie Department of Applied Health Sciences School of Health Sciences College of Medicine and Health University of Birmingham Birmingham United Kingdom Birmingham Biomedical Research Centre United Kingdom Respiratory Evaluation Sciences Program Faculty of Pharmaceutical Sciences The University of British Columbia Vancouver Canada Division of Informatics Imaging and Data Science Faculty of Biology Medicine and Health University of Manchester Manchester Academic Health Science Centre Manchester United Kingdom Centre for Statistics in Medicine Nuffield Department of Orthopaedics Rheumatology and Musculoskeletal Sciences University of Oxford OxfordOX3 7LD United Kingdom

Background Existing sample size calculations for developing clinical prediction models rely on standard (unpenalised) regression-based formula. A general approach is needed for developing or updating a CPM using any statistical or machine learning method. Objectives To propose a general framework for sample size calculations applicable to any model development approach, based on drawing samples from anticipated sampling/posterior distributions and targeting minimal degradation in predictive performance compared to reference model. Methods Researchers must provide candidate predictors, their reference model (e.g., a regression equation matching outcome incidence, predictor weights and c-statistic of previous models), and a (synthetic) dataset reflecting the joint distribution of candidate predictors in the target population. Then, a fully simulation-based approach allows the impact of a chosen development sample size and modelling strategy to be examined. This generates thousands of models and, by applying each to the entire target population, leads to sampling/posterior distributions of individual predictions and model performance (degradation) metrics, to inform required sample sizes. To improve computational speed for penalised regression, we also propose a one-sample Bayesian analysis that combines shrinkage priors with a likelihood decomposed into sample size and Fisher’s unit information. Results The framework is illustrated when developing pre-eclampsia prediction models using logistic regression (unpenalised, uniform shrinkage, lasso or ridge) and random forests. It encompasses existing sample size calculation criteria whilst also providing model assurance probabilities, instability metrics, and degradation statistics about calibration, discrimination, clinical utility, prediction error and fairness. Crucially, the required sample size depends on the users’ key estimands of interest and planned model development or updating approach. Conclusions The new, flex

关键词： Size distribution

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Extracting Kinetic and Stationary Distribution Information from Short MD Trajectories via a Collection of Surrogate Diffusion Models. (vol 5, pg 47, 2009)

引用

JOURNAL OF CHEMICAL THEORY AND COMPUTATION 2009年第8期5卷 2192-2192页

作者： Calderon, Christopher P. Arora, Karunesh Department of Computational and Applied Mathematics and Department of Statistics Rice University Houston Texas 77005-1892 and Department of Chemistry Biophysics Program University of Michigan 930 North University Avenue Ann Arbor Michigan 48109

Low-dimensional stochastic models can summarize dynamical information and make long time predictions associated with observables of complex atomistic systems. Maximum likelihood based techniques for estimating low-dimensional surrogate diffusion models from relatively short time series are presented. It is found that a heterogeneous population of slowly evolving conformational degrees of freedom modulates the dynamics. This underlying heterogeneity results in a collection of estimated low-dimensional diffusion models. Numerical techniques for exploiting this finding to approximate skewed histograms associated with the simulation are presented. In addition, statistical tests are used to assess the validity of the models and determine physically relevant sampling information, e.g. the maximum sampling frequency at which one can discretely sample from an atomistic time series and have a surrogate diffusion model pass goodness-of-fit tests. The information extracted from such analyses can possibly be used to assist umbrella sampling computations as well as help in approximating effective diffusion coefficients. The techniques are demonstrated on simulations of adenylate kinase.

关键词： Transport properties Diffusion Approximation Computational chemistry Computer simulations

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“Select Wisely, Embrace Vitality”: The revision study of nutrition guidelines for later life

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Nutritional Sciences Journal 2024年第1期48卷 13-28页

作者： Lim, Kian Yuan Chan, Yun-Chun Chen, I-Chen Wu, Chao-Chun Chia, Shu-Li Lee, Chia-Hui Chin, Yi-Hua Yang, Feili Lo Department of Nutritional Science Fu Jen Catholic University Taiwan Institute of Applied Statistics Department of Statistics and Information Science Fu Jen Catholic University Taiwan Health Promotion Administration Ministry of Health and Welfare Taiwan Program in Nutrition and Food Science Fu Jen Catholic University Taiwan

Nutrition is a fundamental pillar for fostering healthy aging. This study underscored the process of mixed method research in revising the nutritional guidelines for later life. Dietary habits of older adults were identified using data from the National Food Consumption Database. The nutrient content of dietary recommendations for older adults was found to meet the recommended levels outlined in the Dietary Reference Intakes but not lower calorie recommendations. By integrating the latest research evidence, international experiences, and insights from domestic experts, three key domains were identified to address nutritional and health challenges in later life: healthy eating, disease prevention, and healthy lifestyle. The design of the handbook and flyer for nutrition in later life incorporated user experiences from different target audiences through in-depth interviews, including professional, semi-professional, and non-professional backgrounds. Results of pilot studies and focus groups revealed that most users found the handbook and the flyer practically helpful and easily understandable. In conclusion, the handbook demonstrates theoretical rigor, empirical relevance, and practical utility, making it an essential guide for nutrition in later life for older adults. The experiences gathered from this study offer valuable insights for the future development of nutrition guidelines tailored to various life cycles. © 2024 Nutrition Society in Taiwan. All rights reserved.

关键词： focus group geriatric syndromes in-depth interview mixed method research nutrition through Ute cycles quantitative and qualitative

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