Ying Chen, T. Koch, K. Lim, Xiaofei Xu, Nazgul Zakiyeva
In this data‐rich era, it is essential to develop advanced techniques to analyze and understand large amounts of data and extract the underlying information in a flexible way. We provide a review study on the state‐of‐the‐art statistical time series models for univariate and multivariate functional data with serial dependence. In particular, we review functional autoregressive (FAR) models and their variations under different scenarios. The models include the classic FAR model under stationarity; the FARX and pFAR model dealing with multiple exogenous functional variables and large‐scale mixed‐type exogenous variables; the vector FAR model and common functional principal component technique to handle multiple dimensional functional time series; and the warping FAR, varying coefficient‐FAR and adaptive FAR models to handle seasonal variations, slow varying effects and the more challenging cases of structural changes or breaks respectively. We present the models’ setup and detail the estimation procedure. We discuss the models’ applicability and illustrate the numerical performance using real‐world data of high‐resolution natural gas flows in the high‐pressure gas pipeline network of Germany. We conduct 1‐day and 14‐days‐ahead out‐of‐sample forecasts of the daily gas flow curves. We observe that the functional time series models generally produce stable out‐of‐sample forecast accuracy.
{"title":"A review study of functional autoregressive models with application to energy forecasting","authors":"Ying Chen, T. Koch, K. Lim, Xiaofei Xu, Nazgul Zakiyeva","doi":"10.1002/wics.1525","DOIUrl":"https://doi.org/10.1002/wics.1525","url":null,"abstract":"In this data‐rich era, it is essential to develop advanced techniques to analyze and understand large amounts of data and extract the underlying information in a flexible way. We provide a review study on the state‐of‐the‐art statistical time series models for univariate and multivariate functional data with serial dependence. In particular, we review functional autoregressive (FAR) models and their variations under different scenarios. The models include the classic FAR model under stationarity; the FARX and pFAR model dealing with multiple exogenous functional variables and large‐scale mixed‐type exogenous variables; the vector FAR model and common functional principal component technique to handle multiple dimensional functional time series; and the warping FAR, varying coefficient‐FAR and adaptive FAR models to handle seasonal variations, slow varying effects and the more challenging cases of structural changes or breaks respectively. We present the models’ setup and detail the estimation procedure. We discuss the models’ applicability and illustrate the numerical performance using real‐world data of high‐resolution natural gas flows in the high‐pressure gas pipeline network of Germany. We conduct 1‐day and 14‐days‐ahead out‐of‐sample forecasts of the daily gas flow curves. We observe that the functional time series models generally produce stable out‐of‐sample forecast accuracy.","PeriodicalId":47779,"journal":{"name":"Wiley Interdisciplinary Reviews-Computational Statistics","volume":" ","pages":""},"PeriodicalIF":3.2,"publicationDate":"2020-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/wics.1525","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44328711","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}
Testing for differences between two groups is one of the scenarios most often faced by scientists across all domains and is particularly important in the medical sciences and psychology. The traditional solution to this problem is rooted inside the Neyman–Pearson theory of null hypothesis significance testing and uniformly most powerful tests. In the last decade, a lot of progress has been made in developing Bayesian versions of the most common parametric and nonparametric two‐sample tests, including Student's t‐test and the Mann–Whitney U test. In this article, we review the underlying assumptions, models and implications for research practice of these Bayesian two‐sample tests and contrast them with the existing frequentist solutions. Also, we show that in general Bayesian and frequentist two‐sample tests have different behavior regarding the type I and II error control, which needs to be carefully balanced in practical research.
{"title":"Bayesian and frequentist testing for differences between two groups with parametric and nonparametric two‐sample tests","authors":"Riko Kelter","doi":"10.1002/wics.1523","DOIUrl":"https://doi.org/10.1002/wics.1523","url":null,"abstract":"Testing for differences between two groups is one of the scenarios most often faced by scientists across all domains and is particularly important in the medical sciences and psychology. The traditional solution to this problem is rooted inside the Neyman–Pearson theory of null hypothesis significance testing and uniformly most powerful tests. In the last decade, a lot of progress has been made in developing Bayesian versions of the most common parametric and nonparametric two‐sample tests, including Student's t‐test and the Mann–Whitney U test. In this article, we review the underlying assumptions, models and implications for research practice of these Bayesian two‐sample tests and contrast them with the existing frequentist solutions. Also, we show that in general Bayesian and frequentist two‐sample tests have different behavior regarding the type I and II error control, which needs to be carefully balanced in practical research.","PeriodicalId":47779,"journal":{"name":"Wiley Interdisciplinary Reviews-Computational Statistics","volume":" ","pages":""},"PeriodicalIF":3.2,"publicationDate":"2020-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/wics.1523","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46617382","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}
Digitization as the process of converting information into numbers leads to bigger and more complex data sets, bigger also with respect to the number of measured variables. This makes it harder or impossible for the practitioner to identify outliers or observations that are inconsistent with an underlying model. Classical least‐squares based procedures can be affected by those outliers. In the regression context, this means that the parameter estimates are biased, with consequences on the validity of the statistical inference, on regression diagnostics, and on the prediction accuracy. Robust regression methods aim at assigning appropriate weights to observations that deviate from the model. While robust regression techniques are widely known in the low‐dimensional case, researchers and practitioners might still not be very familiar with developments in this direction for high‐dimensional data. Recently, different strategies have been proposed for robust regression in the high‐dimensional case, typically based on dimension reduction, on shrinkage, including sparsity, and on combinations of such techniques. A very recent concept is downweighting single cells of the data matrix rather than complete observations, with the goal to make better use of the model‐consistent information, and thus to achieve higher efficiency of the parameter estimates.
{"title":"Robust linear regression for high‐dimensional data: An overview","authors":"P. Filzmoser, K. Nordhausen","doi":"10.1002/wics.1524","DOIUrl":"https://doi.org/10.1002/wics.1524","url":null,"abstract":"Digitization as the process of converting information into numbers leads to bigger and more complex data sets, bigger also with respect to the number of measured variables. This makes it harder or impossible for the practitioner to identify outliers or observations that are inconsistent with an underlying model. Classical least‐squares based procedures can be affected by those outliers. In the regression context, this means that the parameter estimates are biased, with consequences on the validity of the statistical inference, on regression diagnostics, and on the prediction accuracy. Robust regression methods aim at assigning appropriate weights to observations that deviate from the model. While robust regression techniques are widely known in the low‐dimensional case, researchers and practitioners might still not be very familiar with developments in this direction for high‐dimensional data. Recently, different strategies have been proposed for robust regression in the high‐dimensional case, typically based on dimension reduction, on shrinkage, including sparsity, and on combinations of such techniques. A very recent concept is downweighting single cells of the data matrix rather than complete observations, with the goal to make better use of the model‐consistent information, and thus to achieve higher efficiency of the parameter estimates.","PeriodicalId":47779,"journal":{"name":"Wiley Interdisciplinary Reviews-Computational Statistics","volume":" ","pages":""},"PeriodicalIF":3.2,"publicationDate":"2020-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/wics.1524","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46937358","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}
The classical modeling of spatial extremes relies on asymptotic models (i.e., max‐stable or r‐Pareto processes) for block maxima or peaks over high thresholds, respectively. However, at finite levels, empirical evidence often suggests that such asymptotic models are too rigidly constrained, and that they do not adequately capture the frequent situation where more severe events tend to be spatially more localized. In other words, these asymptotic models have a strong tail dependence that persists at increasingly high levels, while data usually suggest that it should weaken instead. Another well‐known limitation of classical spatial extremes models is that they are either computationally prohibitive to fit in high dimensions, or they need to be fitted using less efficient techniques. In this review paper, we describe recent progress in the modeling and inference for spatial extremes, focusing on new models that have more flexible tail structures that can bridge asymptotic dependence classes, and that are more easily amenable to likelihood‐based inference for large datasets. In particular, we discuss various types of random scale constructions, as well as the conditional spatial extremes model, which have recently been getting increasing attention within the statistics of extremes community. We illustrate some of these new spatial models on two different environmental applications.
{"title":"Advances in statistical modeling of spatial extremes","authors":"Raphael Huser, J. Wadsworth","doi":"10.1002/wics.1537","DOIUrl":"https://doi.org/10.1002/wics.1537","url":null,"abstract":"The classical modeling of spatial extremes relies on asymptotic models (i.e., max‐stable or r‐Pareto processes) for block maxima or peaks over high thresholds, respectively. However, at finite levels, empirical evidence often suggests that such asymptotic models are too rigidly constrained, and that they do not adequately capture the frequent situation where more severe events tend to be spatially more localized. In other words, these asymptotic models have a strong tail dependence that persists at increasingly high levels, while data usually suggest that it should weaken instead. Another well‐known limitation of classical spatial extremes models is that they are either computationally prohibitive to fit in high dimensions, or they need to be fitted using less efficient techniques. In this review paper, we describe recent progress in the modeling and inference for spatial extremes, focusing on new models that have more flexible tail structures that can bridge asymptotic dependence classes, and that are more easily amenable to likelihood‐based inference for large datasets. In particular, we discuss various types of random scale constructions, as well as the conditional spatial extremes model, which have recently been getting increasing attention within the statistics of extremes community. We illustrate some of these new spatial models on two different environmental applications.","PeriodicalId":47779,"journal":{"name":"Wiley Interdisciplinary Reviews-Computational Statistics","volume":" ","pages":""},"PeriodicalIF":3.2,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/wics.1537","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45974489","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}
Grouping selection arises naturally in many statistical modeling problems. Several group selection methods have been proposed in the last two decades. In this paper, we review the Bayesian group selection approaches for linear regression models. We start from the Bayesian indicator approach and then move to the Bayesian group LASSO methods. In addition, we also consider the Bayesian methods for the sparse group selection that can be treated as an extension of the group selection. Finally, we mention some extensions of Bayesian group selection for the generalized linear models and the multiple response models.
{"title":"A review of Bayesian group selection approaches for linear regression models","authors":"Wei Lai, Ray‐Bing Chen","doi":"10.1002/wics.1513","DOIUrl":"https://doi.org/10.1002/wics.1513","url":null,"abstract":"Grouping selection arises naturally in many statistical modeling problems. Several group selection methods have been proposed in the last two decades. In this paper, we review the Bayesian group selection approaches for linear regression models. We start from the Bayesian indicator approach and then move to the Bayesian group LASSO methods. In addition, we also consider the Bayesian methods for the sparse group selection that can be treated as an extension of the group selection. Finally, we mention some extensions of Bayesian group selection for the generalized linear models and the multiple response models.","PeriodicalId":47779,"journal":{"name":"Wiley Interdisciplinary Reviews-Computational Statistics","volume":" ","pages":""},"PeriodicalIF":3.2,"publicationDate":"2020-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/wics.1513","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43610944","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}
The sufficient dimension reduction of Li has been seen a steady development in the past 30 years in both methodology and application. The main approaches can be categorized into two groups: The inverse regression methods and forward regression methods. In this survey, we briefly discuss advances of methods and present problems that needs further investigation in the second group.
{"title":"Advance of the sufficient dimension reduction","authors":"Weiqiang Hang, Yingcun Xia","doi":"10.1002/wics.1516","DOIUrl":"https://doi.org/10.1002/wics.1516","url":null,"abstract":"The sufficient dimension reduction of Li has been seen a steady development in the past 30 years in both methodology and application. The main approaches can be categorized into two groups: The inverse regression methods and forward regression methods. In this survey, we briefly discuss advances of methods and present problems that needs further investigation in the second group.","PeriodicalId":47779,"journal":{"name":"Wiley Interdisciplinary Reviews-Computational Statistics","volume":" ","pages":""},"PeriodicalIF":3.2,"publicationDate":"2020-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/wics.1516","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42879477","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}
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.
{"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":" ","pages":""},"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}
Pub Date : 2020-05-01Epub Date: 2020-01-17DOI: 10.1002/wics.1495
Karthik Bharath, Sebastian Kurtek
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.
{"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":"12 3","pages":""},"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}
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.
{"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":" ","pages":""},"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}
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