{"title":"30 Years of space–time covariance functions","authors":"E. Porcu, R. Furrer, D. Nychka","doi":"10.1002/wics.1512","DOIUrl":"https://doi.org/10.1002/wics.1512","url":null,"abstract":"In this article, we provide a comprehensive review of space–time covariance functions. As for the spatial domain, we focus on either the d‐dimensional Euclidean space or on the unit d‐dimensional sphere. We start by providing background information about (spatial) covariance functions and their properties along with different types of covariance functions. While we focus primarily on Gaussian processes, many of the results are independent of the underlying distribution, as the covariance only depends on second‐moment relationships. We discuss properties of space–time covariance functions along with the relevant results associated with spectral representations. Special attention is given to the Gneiting class of covariance functions, which has been especially popular in space–time geostatistical modeling. We then discuss some techniques that are useful for constructing new classes of space–time covariance functions. Separate treatment is reserved for spectral models, as well as to what are termed models with special features. We also discuss the problem of estimation of parametric classes of space–time covariance functions. An outlook concludes the paper.","PeriodicalId":47779,"journal":{"name":"Wiley Interdisciplinary Reviews-Computational Statistics","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2020-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/wics.1512","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45698321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Analysis of shape data: From landmarks to elastic curves.","authors":"Karthik Bharath, Sebastian Kurtek","doi":"10.1002/wics.1495","DOIUrl":"10.1002/wics.1495","url":null,"abstract":"<p><p>Proliferation of high-resolution imaging data in recent years has led to sub-stantial improvements in the two popular approaches for analyzing shapes of data objects based on landmarks and/or continuous curves. We provide an expository account of elastic shape analysis of parametric planar curves representing shapes of two-dimensional (2D) objects by discussing its differences, and its commonalities, to the landmark-based approach. Particular attention is accorded to the role of reparameterization of a curve, which in addition to rotation, scaling and translation, represents an important shape-preserving transformation of a curve. The transition to the curve-based approach moves the mathematical setting of shape analysis from finite-dimensional non-Euclidean spaces to infinite-dimensional ones. We discuss some of the challenges associated with the infinite-dimensionality of the shape space, and illustrate the use of geometry-based methods in the computation of intrinsic statistical summaries and in the definition of statistical models on a 2D imaging dataset consisting of mouse vertebrae. We conclude with an overview of the current state-of-the-art in the field.</p>","PeriodicalId":47779,"journal":{"name":"Wiley Interdisciplinary Reviews-Computational Statistics","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2020-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8357314/pdf/nihms-1704274.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39316954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Adversarial machine learning for cybersecurity and computer vision: Current developments and challenges","authors":"B. Xi","doi":"10.1002/wics.1511","DOIUrl":"https://doi.org/10.1002/wics.1511","url":null,"abstract":"We provide a comprehensive overview of adversarial machine learning focusing on two application domains, that is, cybersecurity and computer vision. Research in adversarial machine learning addresses a significant threat to the wide application of machine learning techniques—they are vulnerable to carefully crafted attacks from malicious adversaries. For example, deep neural networks fail to correctly classify adversarial images, which are generated by adding imperceptible perturbations to clean images. We first discuss three main categories of attacks against machine learning techniques—poisoning attacks, evasion attacks, and privacy attacks. Then the corresponding defense approaches are introduced along with the weakness and limitations of the existing defense approaches. We notice adversarial samples in cybersecurity and computer vision are fundamentally different. While adversarial samples in cybersecurity often have different properties/distributions compared with training data, adversarial images in computer vision are created with minor input perturbations. This further complicates the development of robust learning techniques, because a robust learning technique must withstand different types of attacks.","PeriodicalId":47779,"journal":{"name":"Wiley Interdisciplinary Reviews-Computational Statistics","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2020-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/wics.1511","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43224376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Nonparametric covariance estimation with shrinkage toward stationary models","authors":"T. A. Blake, Yoonkyung Lee","doi":"10.1002/wics.1507","DOIUrl":"https://doi.org/10.1002/wics.1507","url":null,"abstract":"Estimation of an unstructured covariance matrix is difficult because of the challenges posed by parameter space dimensionality and the positive‐definiteness constraint that estimates should satisfy. We consider a general nonparametric covariance estimation framework for longitudinal data using the Cholesky decomposition of a positive‐definite matrix. The covariance matrix of time‐ordered measurements is diagonalized by a lower triangular matrix with unconstrained entries that are statistically interpretable as parameters for a varying coefficient autoregressive model. Using this dual interpretation of the Cholesky decomposition and allowing for irregular sampling time points, we treat covariance estimation as bivariate smoothing and cast it in a regularization framework for desired forms of simplicity in covariance models. Viewing stationarity as a form of simplicity or parsimony in covariance, we model the varying coefficient function with components depending on time lag and its orthogonal direction separately and penalize the components that capture the nonstationarity in the fitted function. We demonstrate construction of a covariance estimator using the smoothing spline framework. Simulation studies establish the advantage of our approach over alternative estimators proposed in the longitudinal data setting. We analyze a longitudinal dataset to illustrate application of the methodology and compare our estimates to those resulting from alternative models.","PeriodicalId":47779,"journal":{"name":"Wiley Interdisciplinary Reviews-Computational Statistics","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2020-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/wics.1507","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47761789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Review of current advances in survival analysis and frailty models","authors":"Usha Govindarajulu, R. D'Agostino","doi":"10.1002/wics.1504","DOIUrl":"https://doi.org/10.1002/wics.1504","url":null,"abstract":"In this article, we have presented a review of existing methods and trends in survival analysis and frailty models. The background has been presented for each topic discussed for survival and frailty models where the presentation flows from original methods to more advanced methods. This article has also shown various current methodologies that exist among survival and frailty models. The advantages and disadvantages of more recent methodologies are presented and discussed in this review.","PeriodicalId":47779,"journal":{"name":"Wiley Interdisciplinary Reviews-Computational Statistics","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2020-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/wics.1504","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41737607","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Bayesian spatial and spatiotemporal models based on multiscale factorizations","authors":"Marco A. R. Ferreira","doi":"10.1002/wics.1509","DOIUrl":"https://doi.org/10.1002/wics.1509","url":null,"abstract":"We review the literature on spatial and spatiotemporal models based on spatial multiscale factorizations. Specifically, we review models based on wavelets and Kolaczyk–Huang factorizations for Gaussian and Poisson data. These multiscale models decompose spatial and spatiotemporal datasets into many small components, called multiscale coefficients, at multiple levels of spatial resolution. Then analysis proceeds independently for each multiscale coefficient. After that, aggregation equations are used to coherently combine the analyses from the multiple multiscale coefficients to obtain a statistical analysis at the original resolution level. The computational cost of such analysis grows linearly with sample size. Furthermore, computations for these models are scalable, parallelizable, and fast. Therefore, these multiscale models are tremendously useful for the analysis of massive spatial and spatiotemporal datasets.","PeriodicalId":47779,"journal":{"name":"Wiley Interdisciplinary Reviews-Computational Statistics","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2020-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/wics.1509","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47673378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Animal movement models for multiple individuals","authors":"H. Scharf, F. Buderman","doi":"10.1002/wics.1506","DOIUrl":"https://doi.org/10.1002/wics.1506","url":null,"abstract":"Statistical models for animal movement provide tools that help ecologists and biologists learn how animals interact with their environment and each other. Efforts to develop increasingly realistic, implementable, and scientifically valuable methods for analyzing remotely observed trajectories have provided practitioners with a wide selection of models to help them understand animal behavior. Increasingly, researchers are interested in studying multiple animals jointly, which requires methods that can account for dependence across individuals. Dependence can arise for many reasons, including shared behavioral tendencies, familial relationships, and direct interactions on the landscape. We provide a synopsis of recent statistical methods for animal movement data applicable to settings in which inference is desired across multiple individuals. Highlights of these approaches include the ability to infer shared behavioral traits across a group of individuals and the ability to infer unobserved social networks summarizing dynamic relationships that manifest themselves in movement decisions.","PeriodicalId":47779,"journal":{"name":"Wiley Interdisciplinary Reviews-Computational Statistics","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2020-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/wics.1506","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45395796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A review of flow field forecasting: A high‐dimensional forecasting procedure","authors":"Kyle A. Caudle, Patrick S. Fleming, R. Hoover","doi":"10.1002/wics.1505","DOIUrl":"https://doi.org/10.1002/wics.1505","url":null,"abstract":"Forecasting, especially high‐dimensional forecasting, is becoming more and more sought after, particularly as computing resources increase in both size and speed. Flow field forecasting is a general purpose regression‐based forecasting method that has recently been expanded to high‐dimensional settings. In this article, we provide an overview of the flow field forecasting methodology, with a particular emphasis on environments where the number of candidate predictor variables is large, potentially larger than the number of observations.","PeriodicalId":47779,"journal":{"name":"Wiley Interdisciplinary Reviews-Computational Statistics","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2020-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/wics.1505","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42758852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}