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- Volume 7, 2020
Annual Review of Statistics and Its Application - Volume 7, 2020
Volume 7, 2020
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Statistical Significance
Vol. 7 (2020), pp. 1–10More LessA broad review is given of the role of statistical significance tests in the analysis of empirical data. Four main types of application are outlined. The first, conceptually quite different from the others, concerns decision making in such contexts as medical screening and industrial inspection. The others assess the security of conclusions. The article concludes with an outline discussion of some more specialized points.
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Calibrating the Scientific Ecosystem Through Meta-Research
Vol. 7 (2020), pp. 11–37More LessWhile some scientists study insects, molecules, brains, or clouds, other scientists study science itself. Meta-research, or research-on-research, is a burgeoning discipline that investigates efficiency, quality, and bias in the scientific ecosystem, topics that have become especially relevant amid widespread concerns about the credibility of the scientific literature. Meta-research may help calibrate the scientific ecosystem toward higher standards by providing empirical evidence that informs the iterative generation and refinement of reform initiatives. We introduce a translational framework that involves (a) identifying problems, (b) investigating problems, (c) developing solutions, and (d) evaluating solutions. In each of these areas, we review key meta-research endeavors and discuss several examples of prior and ongoing work. The scientific ecosystem is perpetually evolving; the discipline of meta-research presents an opportunity to use empirical evidence to guide its development and maximize its potential.
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The Role of Statistical Evidence in Civil Cases
Vol. 7 (2020), pp. 39–60More LessCivil cases outnumber criminal cases in federal courts, and statistical evidence has become more important in a wide variety of them. In contrast to science, which is concerned with general phenomena, legal cases concern one plaintiff or a class of plaintiffs and replication of the events that led to the case is not possible. This review describes the legal process, the way statistics are used in several types of cases, and the criteria courts use in evaluating the reliability of statistical testimony. Several examples of courts’ misinterpreting statistical analyses are presented. Commonly occurring issues in the statistical analysis of stratified data, the use of regression analysis, and the use of epidemiologic estimates of relative risk are described. Hopefully, this review will encourage statisticians to engage with the legal system and develop better ways of communicating the results of studies so they receive the evidentiary weight they deserve.
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Testing Statistical Charts: What Makes a Good Graph?
Vol. 7 (2020), pp. 61–88More LessIt has been approximately 100 years since the very first formal experimental evaluations of statistical charts were conducted. In that time, technological changes have impacted both our charts and our testing methods, resulting in a dizzying array of charts, many different taxonomies to classify graphics, and several different philosophical approaches to testing the efficacy of charts and graphs experimentally. Once rare, charts and graphical displays are now everywhere—but do they help us understand? In this article we review the history of graphical testing across disciplines, discuss different direct approaches to testing graphics, and contrast direct tests with visual inference, which requires that the viewer determine both the question and the answer. Examining the past 100 years of graphical testing, we summarize best practices for creating effective graphics and discuss what the future holds for graphics and empirical testing of interactive statistical visualizations.
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Statistical Methods for Extreme Event Attribution in Climate Science
Vol. 7 (2020), pp. 89–110More LessChanges in the Earth's climate have been increasingly observed. Assessing the likelihood that each of these changes has been caused by human influence is important for decision making on mitigation and adaptation policy. Because of their large societal and economic impacts, extreme events have garnered much media attention—have they become more frequent and more intense, and if so, why? To answer such questions, extreme event attribution (EEA) tries to estimate extreme event likelihoods under different scenarios. Over the past decade, statistical methods and experimental designs based on numerical models have been developed, tested, and applied. In this article, we review the basic probability schemes, inference techniques, and statistical hypotheses used in EEA. To implement EEA analysis, the climate community relies on the use of large ensembles of climate model runs. We discuss, from a statistical perspective, how extreme value theory could help to deal with the different modeling uncertainties. In terms of interpretation, we stress that causal counterfactual theory offers an elegant framework that clarifies the design of event attributions. Finally, we pinpoint some remaining statistical challenges, including the choice of the appropriate spatio-temporal scales to enhance attribution power, the modeling of concomitant extreme events in a multivariate context, and the coupling of multi-ensemble and observational uncertainties.
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DNA Mixtures in Forensic Investigations: The Statistical State of the Art
Vol. 7 (2020), pp. 111–142More LessForensic science has experienced a period of rapid change because of the tremendous evolution in DNA profiling. Problems of forensic identification from DNA evidence can become extremely challenging, both logically and computationally, in the presence of complicating features, such as in mixed DNA trace evidence. Additional complicating aspects are possible, such as missing data on individuals, heterogeneous populations, and kinship. In such cases, there is considerable uncertainty involved in determining whether or not the DNA of a given individual is actually present in the sample. We begin by giving a brief introduction to the genetic background needed for understanding forensic DNA mixtures, including the artifacts that commonly occur in the DNA amplification process. We then review different methods and software based on qualitative and quantitative information and give details on a quantitative method that uses Bayesian networks as a computational device for efficiently computing likelihoods. This method allows for the possibility of combining evidence from multiple samples to make inference about relationships from DNA mixtures and other more complex scenarios.
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Modern Algorithms for Matching in Observational Studies
Vol. 7 (2020), pp. 143–176More LessUsing a small example as an illustration, this article reviews multivariate matching from the perspective of a working scientist who wishes to make effective use of available methods. The several goals of multivariate matching are discussed. Matching tools are reviewed, including propensity scores, covariate distances, fine balance, and related methods such as near-fine and refined balance, exact and near-exact matching, tactics addressing missing covariate values, the entire number, and checks of covariate balance. Matching structures are described, such as matching with a variable number of controls, full matching, subset matching and risk-set matching. Software packages in R are described. A brief review is given of the theory underlying propensity scores and the associated sensitivity analysis concerning an unobserved covariate omitted from the propensity score.
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Randomized Experiments in Education, with Implications for Multilevel Causal Inference
Vol. 7 (2020), pp. 177–208More LessEducation research has experienced a methodological renaissance over the past two decades, with a new focus on large-scale randomized experiments. This wave of experiments has made education research an even more exciting area for statisticians, unearthing many lessons and challenges in experimental design, causal inference, and statistics more broadly. Importantly, educational research and practice almost always occur in a multilevel setting, which makes the statistics relevant to other fields with this structure, including social policy, health services research, and clinical trials in medicine. In this article we first briefly review the history that led to this new era in education research and describe the design features that dominate the modern large-scale educational experiments. We then highlight some of the key statistical challenges in this area, including endogeneity of design, heterogeneity of treatment effects, noncompliance with treatment assignment, mediation, generalizability, and spillover. Though a secondary focus, we also touch on promising trial designs that answer more nuanced questions, such as the SMART design for studying dynamic treatment regimes and factorial designs for optimizing the components of an existing treatment.
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A Survey of Tuning Parameter Selection for High-Dimensional Regression
Vol. 7 (2020), pp. 209–226More LessPenalized (or regularized) regression, as represented by lasso and its variants, has become a standard technique for analyzing high-dimensional data when the number of variables substantially exceeds the sample size. The performance of penalized regression relies crucially on the choice of the tuning parameter, which determines the amount of regularization and hence the sparsity level of the fitted model. The optimal choice of tuning parameter depends on both the structure of the design matrix and the unknown random error distribution (variance, tail behavior, etc.). This article reviews the current literature of tuning parameter selection for high-dimensional regression from both the theoretical and practical perspectives. We discuss various strategies that choose the tuning parameter to achieve prediction accuracy or support recovery. We also review several recently proposed methods for tuning-free high-dimensional regression.
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Algebraic Statistics in Practice: Applications to Networks
Vol. 7 (2020), pp. 227–250More LessAlgebraic statistics uses tools from algebra (especially from multilinear algebra, commutative algebra, and computational algebra), geometry, and combinatorics to provide insight into knotty problems in mathematical statistics. In this review, we illustrate this on three problems related to networks: network models for relational data, causal structure discovery, and phylogenetics. For each problem, we give an overview of recent results in algebraic statistics, with emphasis on the statistical achievements made possible by these tools and their practical relevance for applications to other scientific disciplines.
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Bayesian Additive Regression Trees: A Review and Look Forward
Vol. 7 (2020), pp. 251–278More LessBayesian additive regression trees (BART) provides a flexible approach to fitting a variety of regression models while avoiding strong parametric assumptions. The sum-of-trees model is embedded in a Bayesian inferential framework to support uncertainty quantification and provide a principled approach to regularization through prior specification. This article presents the basic approach and discusses further development of the original algorithm that supports a variety of data structures and assumptions. We describe augmentations of the prior specification to accommodate higher dimensional data and smoother functions. Recent theoretical developments provide justifications for the performance observed in simulations and other settings. Use of BART in causal inference provides an additional avenue for extensions and applications. We discuss software options as well as challenges and future directions.
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Q-Learning: Theory and Applications
Jesse Clifton, and Eric LaberVol. 7 (2020), pp. 279–301More LessQ-learning, originally an incremental algorithm for estimating an optimal decision strategy in an infinite-horizon decision problem, now refers to a general class of reinforcement learning methods widely used in statistics and artificial intelligence. In the context of personalized medicine, finite-horizon Q-learning is the workhorse for estimating optimal treatment strategies, known as treatment regimes. Infinite-horizon Q-learning is also increasingly relevant in the growing field of mobile health. In computer science, Q-learning methods have achieved remarkable performance in domains such as game-playing and robotics. In this article, we (a) review the history of Q-learning in computer science and statistics, (b) formalize finite-horizon Q-learning within the potential outcomes framework and discuss the inferential difficulties for which it is infamous, and (c) review variants of infinite-horizon Q-learning and the exploration-exploitation problem, which arises in decision problems with a long time horizon. We close by discussing issues arising with the use of Q-learning in practice, including arguments for combining Q-learning with direct-search methods; sample size considerations for sequential, multiple assignment randomized trials; and possibilities for combining Q-learning with model-based methods.
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Representation Learning: A Statistical Perspective
Vol. 7 (2020), pp. 303–335More LessLearning representations of data is an important problem in statistics and machine learning. While the origin of learning representations can be traced back to factor analysis and multidimensional scaling in statistics, it has become a central theme in deep learning with important applications in computer vision and computational neuroscience. In this article, we review recent advances in learning representations from a statistical perspective. In particular, we review the following two themes: (a) unsupervised learning of vector representations and (b) learning of both vector and matrix representations.
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Robust Small Area Estimation: An Overview
Jiming Jiang, and J. Sunil RaoVol. 7 (2020), pp. 337–360More LessA small area typically refers to a subpopulation or domain of interest for which a reliable direct estimate, based only on the domain-specific sample, cannot be produced due to small sample size in the domain. While traditional small area methods and models are widely used nowadays, there have also been much work and interest in robust statistical inference for small area estimation (SAE). We survey this work and provide a comprehensive review here. We begin with a brief review of the traditional SAE methods. We then discuss SAE methods that are developed under weaker assumptions and SAE methods that are robust in certain ways, such as in terms of outliers or model failure. Our discussion also includes topics such as nonparametric SAE methods, Bayesian approaches, model selection and diagnostics, and missing data. A brief review of software packages available for implementing robust SAE methods is also given.
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Nonparametric Spectral Analysis of Multivariate Time Series
Vol. 7 (2020), pp. 361–386More LessSpectral analysis of multivariate time series has been an active field of methodological and applied statistics for the past 50 years. Since the success of the fast Fourier transform algorithm, the analysis of serial auto- and cross-correlation in the frequency domain has helped us to understand the dynamics in many serially correlated data without necessarily needing to develop complex parametric models. In this work, we give a nonexhaustive review of the mostly recent nonparametric methods of spectral analysis of multivariate time series, with an emphasis on model-based approaches. We try to give insights into a variety of complimentary approaches for standard and less standard situations (such as nonstationary, replicated, or high-dimensional time series), discuss estimation aspects (such as smoothing over frequency), and include some examples stemming from life science applications (such as brain data).
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Convergence Diagnostics for Markov Chain Monte Carlo
Vol. 7 (2020), pp. 387–412More LessMarkov chain Monte Carlo (MCMC) is one of the most useful approaches to scientific computing because of its flexible construction, ease of use, and generality. Indeed, MCMC is indispensable for performing Bayesian analysis. Two critical questions that MCMC practitioners need to address are where to start and when to stop the simulation. Although a great amount of research has gone into establishing convergence criteria and stopping rules with sound theoretical foundation, in practice, MCMC users often decide convergence by applying empirical diagnostic tools. This review article discusses the most widely used MCMC convergence diagnostic tools. Some recently proposed stopping rules with firm theoretical footing are also presented. The convergence diagnostics and stopping rules are illustrated using three detailed examples.
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