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Uncertainty quantification for climate observations

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Uncertainty quantification for climate observations

作者： Matthews, Jessica L. Mannshardt, Elizabeth Gremaud, Pierre Cooperative Institute for Climate and Satellites North Carolina State University NOAA's National Climatic Data Center 151 Patton Avenue Asheville NC 28801 United States Program in Spatial Statistics and Environmental Statistics Ohio State University Columbus OH United States Statistical and Applied Mathematical Sciences Institute Research Triangle Park NC United States Department of Statistics North Carolina State University Raleigh NC United States

Experts suggest that Observations are key to uncertainty quantification (UQ) in climate research as they form the very basis for any evidence of climate change and provide a source of information about the way in which physical processes are modeled and understood. The uncertainties in climate observations pose a set of methodological and practical challenges for both the analysis of long-term trends and the comparison between data and model simulations. A workshop has been organized in January 2012 to discuss the issues surrounding uncertainty quantification in the context of climate observations. This workshop provides an opportunity to engage with and understand the different concerns and perspectives from the academic mathematical and statistical communities and climate data product scientists and providers. Major results of the event include the realization of interest in collaboration and identification of possible steps to work toward the mutual goal of characterizing uncertainty in climate observation.

关键词： Climate change

Neural Bayes estimators for censored inference with peaks-over-threshold models

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The Journal of Machine Learning Research

The Journal of Machine Learning Research 2024年第1期25卷 19070-19118页

作者： Jordan Richards Matthew Sainsbury-Dale Andrew Zammit-Mangion Raphaël Huser School of Mathematics and Maxwell Institute for Mathematical Sciences University of Edinburgh Edinburgh UK and Statistics Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology (KAUST) Thuwal Saudi Arabia Statistics Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology (KAUST) Thuwal Saudi Arabia and School of Mathematics and Applied Statistics University of Wollongong Wollongong Australia School of Mathematics and Applied Statistics University of Wollongong Wollongong Australia Statistics Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology (KAUST) Thuwal Saudi Arabia

Making inference with spatial extremal dependence models can be computationally burdensome since they involve intractable and/or censored likelihoods. Building on recent advances in likelihood-free inference with neural Bayes estimators, that is, neural networks that approximate Bayes estimators, we develop highly efficient estimators for censored peaks-over-threshold models that use augmented data to encode censoring information in the neural network input. Our new method provides a paradigm shift that challenges traditional censored likelihood-based inference methods for spatial extremal dependence models. Our simulation studies highlight significant gains in both computational and statistical efficiency, relative to competing likelihood-based approaches, when applying our novel estimators to make inference with popular extremal dependence models, such as max-stable, r-Pareto, and random scale mixture process models. We also illustrate that it is possible to train a single neural Bayes estimator for a general censoring level, precluding the need to retrain the network when the censoring level is changed. We illustrate the efficacy of our estimators by making fast inference on hundreds-of-thousands of high-dimensional spatial extremal dependence models to assess extreme particulate matter 2.5 microns or less in diameter (PM2:5) concentration over the whole of Saudi Arabia.

关键词： censored data convolutional neural network likelihood-free inference neural estimation spatial extremes threshold exceedance

Temporal and phenological profiles of open and dense Caatinga using remote sensing:response to precipitation and its irregularities

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Journal of Forestry Research 2021年第3期32卷 1067-1076页

作者： Janisson Batista de Jesus Tatiana Mora Kuplich íkaro Daniel de Carvalho Barreto Cristiano Niederauer da Rosa Fernando Luis Hillebrand Postgraduate Program in Remote Sensing Federal University of Rio Grande Do SulAv.Bento GoncalvesCEP 91501-970Porto AlegreRio Grande do Sul 9500Brazil National Institute for Space Research(INPE)Southern Regional Centre(CRS) CEP 97105-970Santa MariaRio Grande do SulBrazil Postgraduate Program in Applied Biometrics and Statistics Rural Federal University of PernambucoDom Manuel de Medeiross/nDois IrmaosCEP 52171-900RecifePernambucoBrazil

Caatinga is a typical biome of Brazil's semiarid regions and subject to climate *** is needed on the relation of its features to climate *** study analyzed the infl uence of rainfall and its irregularities in open and dense woody Caatinga *** curves were generated by means of Normalized Difference Vegetation Index(NDVI)time profiles in the Grota do Angico Conservation Unit study area in Sergipe *** data from 2000 to 2018 were collected and phenological curves generated using various estimate methods that produced the following variables:[start of season,end of season,peak of season position,length of season,mean growing season and maximum seasonal].Rainfall showed a standard intra-annual behavior,with inter-annual variations related to irregularities infl uencing Caatinga *** Caatinga vegetation had higher values of NDVI in all periods,even in anomalous years compared to open Caatinga,in addition to having longer leaf coverage over the year,with an anticipated start and a more extended seasonal *** analysis of the rainfall regime made it possible to assess its infl uence on the Caatinga and phenological profiles proved to be fundamental to understand periods of physiological change of open and dense *** results indicate that dense Caatinga maintains physiological activity longer,which may be associated with greater moisture maintenance in a semiarid *** addition,because it has a greater leaf cover for longer periods,the soil may be preserved and maintain its characteristics longer,reducing the effects of *** results may be associated with the type of forest management and conservation in this *** total or partial suppression of individual remnants of Caatinga should be avoided,since the most open areas have lower photosynthetic capacity,affected to a considerable extent from the effects of adverse climatic ***,open Caatinga has a reduced cap

关键词： Semiarid Tropical dry forest NDVI MODIS Phenopix

Null Space Properties of Neural Networks with Applications to Image Steganography

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arXiv 2023年

作者： Li, Xiang Short, Kevin M. Integrated Applied Mathematics Program Department of Mathematics and Statistics University of New Hampshire DurhamNH03824 United States

This paper explores the null space properties of neural networks. We extend the null space definition from linear to nonlinear maps and discuss the presence of a null space in neural networks. The null space of a given neural network can tell us the part of the input data that makes no contribution to the final prediction so that we can use it to trick the neural network. This reveals an inherent weakness in neural networks that can be exploited. One application described here leads to a method of image steganography. Through experiments on image datasets such as MNIST, we show that we can use null space components to force the neural network to choose a selected hidden image class, even though the overall image can be made to look like a completely different image. We conclude by showing comparisons between what a human viewer would see, and the part of the image that the neural network is actually using to make predictions and, hence, show that what the neural network "sees" is completely different than what we would expect. Copyright © 2023, The Authors. All rights reserved.

关键词： Machine learning

A Neural Network-Based Approach to Normality Testing for Dependent Data

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arXiv 2023年

作者： Kim, Minwoo Genton, Marc G. Huser, Raphaël Castruccio, Stefano Department of Statistics Pusan National University Korea Republic of Statistics program King Abdullah University of Science and Technology Saudi Arabia Department of Applied and Computational Mathematics and Statistics University of Notre Dame United States

There is a wide availability of methods for testing normality under the assumption of independent and identically distributed data. When data are dependent in space and/or time, however, assessing and testing the marginal behavior is considerably more challenging, as the marginal behavior is impacted by the degree of dependence. We propose a new approach to assess normality for dependent data by non-linearly incorporating existing statistics from normality tests as well as sample moments such as skewness and kurtosis through a neural network. We calibrate (deep) neural networks by simulated normal and non-normal data with a wide range of dependence structures and we determine the probability of rejecting the null hypothesis. We compare several approaches for normality tests and demonstrate the superiority of our method in terms of statistical power through an extensive simulation study. A real world application to global temperature data further demonstrates how the degree of spatio-temporal aggregation affects the marginal normality in the data. © 2023, CC BY.

关键词： Higher order statistics

Spatial Bayesian Neural Networks

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arXiv 2023年

作者： Zammit-Mangion, Andrew Kaminski, Michael D. Tran, Ba-Hien Filippone, Maurizio Cressie, Noel School of Mathematics and Applied Statistics University of Wollongong Australia Paris Research Centre Huawei Technologies France Statistics Program King Abdullah University of Science and Technology Saudi Arabia

Statistical models for spatial processes play a central role in analyses of spatial data. Yet, it is the simple, interpretable, and well understood models that are routinely employed even though, as is revealed through prior and posterior predictive checks, these can poorly characterise the spatial heterogeneity in the underlying process of interest. Here, we propose a new, flexible class of spatial-process models, which we refer to as spatial Bayesian neural networks (SBNNs). An SBNN leverages the representational capacity of a Bayesian neural network;it is tailored to a spatial setting by incorporating a spatial "embedding layer" into the network and, possibly, spatially-varying network parameters. An SBNN is calibrated by matching its finite-dimensional distribution at locations on a fine gridding of space to that of a target process of interest. That process could be easy to simulate from or we may have many realisations from it. We propose several variants of SBNNs, most of which are able to match the finite-dimensional distribution of the target process at the selected grid better than conventional BNNs of similar complexity. We also show that an SBNN can be used to represent a variety of spatial processes often used in practice, such as Gaussian processes, lognormal processes, and max-stable processes. We briefly discuss the tools that could be used to make inference with SBNNs, and we conclude with a discussion of their advantages and limitations. Copyright © 2023, The Authors. All rights reserved.

关键词： Bayesian networks

ON A LINEARIZATION OF QUADRATIC WASSERSTEIN DISTANCE

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arXiv 2022年

作者： Greengard, Philip Hoskins, Jeremy G. Marshall, Nicholas F. Singer, Amit Department of Statistics Columbia University United States Department of Statistics University of Chicago United States Program in Applied and Computational Mathematics The Department of Mathematics Princeton University United States

This paper studies the problem of computing a linear approximation of quadratic Wasserstein distance W2. In particular, we compute an approximation of the negative homogeneous weighted Sobolev norm whose connection to Wasserstein distance follows from a classic linearization of a general Monge-Ampére equation. Our contribution is threefold. First, we provide expository material on this classic linearization of Wasserstein distance including a quantitative error estimate. Second, we reduce the computational problem to solving a elliptic boundary value problem involving the Witten Laplacian, which is a Schrödinger operator of the form H = -∆ + V , and describe an associated embedding. Third, for the case of probability distributions on the unit square [0, 1]2 represented by n × n arrays we present a fast code demonstrating our approach. Several numerical examples are presented. Copyright © 2022, The Authors. All rights reserved.

关键词： Laplace transforms

STATISTICAL ISSUES AND PROBLEMS IN GROUND-WATER DETECTION MONITORING AT HAZARDOUS-WASTE FACILITIES

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GROUND WATER MONITORING AND REMEDIATION 1988年第4期8卷 135-150页

作者： MCNICHOLS, RJ DAVIS, CB Roger J. McNichols is a professor of industrial engineering at the University of Toledo (Department of Industrial Engineering University of Toledo Toledo OH 43606). After receiving his Ph.D in industrial engineering from The Ohio State University he joined the faculty of Texas A and M University where he directed the Maintainability Engineering Graduate Program at Red River Army Depot. At UT he has served as associate dean of engineering and as chairman of the Systems engineering doctoral program. His research and consulting interests include reliability quality control manufacturing mathematical modeling and applied statistics. Charles B. Davis is an associate professor of mathematics at the University of Toledo (Department of Mathematics University of Toledo Toledo OH 43606). After receiving his M.S. in mathematics and statistics and his Ph.D. in statistics from the University of New Mexico he joined the Mathematics Department at UT where he established the graduate program in statistics. His research and consulting interests include statistical modeling statistical computation simultaneous inference and data analysis.

Ground water monitoring presents interesting statistical challenges, including controlling the risk of entering compliance monitoring, incorporating all modes of inherent variability into the statistical model on which tests are based, and taming the detection limit problem, all while maintaining demonstrable sensitivity to real contamination. Some of these challenges exceed textbook statistics considerably, even when considered alone, and good solutions are scarce. When these challenges are combined, the task of developing good statistical procedures or good regulations can be formidable. This article presents a number of realities of ground water monitoring that should be considered when developing statistical procedures. Recommendations made for addressing these realities include the following: (1) the false positive rate should be controlled on a facility-wide basis, rather than per well or per parameter as required in the proposed regulation (40 CFR §264); (2) multiple comparisons with control procedures are preferable to analysis of variance (ANOVA) for controlling the overall false positive rate; (3) retests can be made an explicit part of the statistical procedure in order to increase power and decrease sensitivity to distribution shape assumptions; (4) commonly used simple methods of handling below detection limit data with parametric tests, including Cohen's procedure as implemented in the U.S. EPA's Technical Enforcement Guidance Document (TEGD), should probably be avoided; (5) the statistical properties of practical quantitation limits for non-naturally occurring compounds should be studied carefully; and (6) so long as the facility-wide false positive rate is controlled, better sensitivity to real contamination is obtained by monitoring fewer well-chosen parameters at a smaller number of well-chosen locations. An evaluation of the proposed revised §264 regulation with respect to these realities reveals that it seems to be a definite improvement over the

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Robust analysis of related samples under the presence of population substructure

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Robust analysis of related samples under the presence of pop...

IEEE International Conference on Bioinformatics and Biomedicine Workshops (BIBMW)

作者： Sungkyoung Choi Sungho Won Bioinformatics Program Seoul National University Seoul South Korea Department of Applied Statistics Chung-Ang University Seoul South Korea

We propose a new method for genome-wide association analysis with a family-based design. The proposed method is robust against population substructure while it is more efficient than the traditional method such as transmission disequilibrium test for related samples. The proposed method estimates the correlation matrix between individuals and then the principal component analysis is applied. To maximize the statistical power, we consider the additive polygenic model and a best linear unbiased predictor is used as offset. We confirmed that the proposed method is always efficient by simulation studies. The method will be applied to Framingham Heart study.

关键词： Bioinformatics Genomics Diseases Correlation Robustness Testing