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Multivariate time series data collected extensively from the real world allows us to observe urban phenomena on an unprecedented scale. However, recovering the underlying causal relations from these observations remains a challenging task, as these causal relations tend to be time-varying. Previous methods have extracted a causal graph over a long period of observation, but cannot be directly applied to capture, interpret, and verify dynamic causal relations. In this paper, we propose a novel visual analysis method for in-depth analysis of dynamic causal relations in multivariate time series. To address the following three challenges: detecting causality, explaining dynamic causality, and uncovering questionable causality, we design and develop the interactive visual analysis system MTCausal. First, a causal detection framework based on Granger causality test is used to obtain the time-varying causal relations in multivariate time series. Then, a dynamic causal graph visualization is designed to explore and interpret these causal graphs over time. Finally, a set of novel visualizations and interactions are designed to support the validation and comparison of causal relations to improve the results of causal analysis. The effectiveness of MTCausal is evaluated through the case studies on the real-world air pollution dataset, which demonstrate that users can effectively explore and analyze dynamic causal relationships. Graphic Abstract

Observational databases are often used to study causal questions. Before being granted access to data or funding, researchers may need to prove that “the statistical power of their analysis will be high.” Analyses expected to have low power, and hence result in imprecise estimates, will not be approved. This restrictive attitude towards observational analyses is misguided. A key misunderstanding is the belief that the goal of a causal analysis is to “detect” an effect. Causal effects are not binary signals that are either detected or undetected; causal effects are numerical quantities that need to be estimated. Because the goal is to quantify the effect as unbiasedly and precisely as possible, the solution to observational analyses with imprecise effect estimates is not avoiding observational analyses with imprecise estimates, but rather encouraging the conduct of many observational analyses. It is preferable to have multiple studies with imprecise estimates than having no study at all. After several studies become available, we will meta-analyze them and provide a more precise pooled effect estimate. Therefore, the justification to withhold an observational analysis of preexisting data cannot be that our estimates will be imprecise. Ethical arguments for power calculations before conducting a randomized trial which place individuals at risk are not transferable to observational analyses of existing databases. If a causal question is important, analyze your data, publish your estimates, encourage others to do the same, and then meta-analyze. The alternative is an unanswered question.

Recent discussions of model selection and multimodel inference highlight a general challenge for researchers: how to convey the explanatory content of a hypothesized model or set of competing models clearly. The advice from statisticians for scientists employing multimodel inference is to develop a well-thought-out set of candidate models for comparison, though precise instructions for how to do that are typically not given. A coherent body of knowledge, which falls under the general term causal analysis, now exists for examining the explanatory scientific content of candidate models. Much of the literature on causal analysis has been recently developed, and we suspect may not be familiar to many ecologists. This body of knowledge comprises a set of graphical tools and axiomatic principles to support scientists in their endeavors to create “well-formed hypotheses,” as statisticians are asking them to do. Causal analysis is complementary to methods such as structural equation modeling, which provides the means for evaluation of proposed hypotheses against data. In this paper, we summarize and illustrate a set of principles that can guide scientists in their quest to develop explanatory hypotheses for evaluation. The principles presented in this paper have the capacity to close the communication gap between statisticians, who urge scientists to develop well-thought-out coherent models, and scientists, who would like some practical advice for exactly how to do that.

Independent component analysis is a probabilistic method for learning a linear transform of a random vector. The goal is to find components that are maximally independent and non-Gaussian (non-normal). Its fundamental difference to classical multi-variate statistical methods is in the assumption of non-Gaussianity, which enables the identification of original, underlying components, in contrast to classical methods. The basic theory of independent component analysis was mainly developed in the 1990s and summarized, for example, in our monograph in 2001. Here, we provide an overview of some recent developments in the theory since the year 2000. The main topics are: analysis of causal relations, testing independent components, analysing multiple datasets (three-way data), modelling dependencies between the components and improved methods for estimating the basic model.

Structural equation modeling (SEM) is increasingly being chosen by researchers as a framework for gaining scientific insights from the quantitative analyses of data. New ideas and methods emerging from the study of causality, influences from the field of graphical modeling, and advances in statistics are expanding the rigor, capability, and even purpose of SEM. Guidelines for implementing the expanded capabilities of SEM are currently lacking. In this paper we describe new developments in SEM that we believe constitute a third-generation of the methodology. Most characteristic of this new approach is the generalization of the structural equation model as a causal graph. In this generalization, analyses are based on graph theoretic principles rather than analyses of matrices. Also, new devices such as metamodels and causal diagrams, as well as an increased emphasis on queries and probabilistic reasoning, are now included. Estimation under a graph theory framework permits the use of Bayesian or likelihood methods. The guidelines presented start from a declaration of the goals of the analysis. We then discuss how theory frames the modeling process, requirements for causal interpretation, model specification choices, selection of estimation method, model evaluation options, and use of queries, both to summarize retrospective results and for prospective analyses. The illustrative example presented involves monitoring data from wetlands on Mount Desert Island, home of Acadia National Park. Our presentation walks through the decision process involved in developing and evaluating models, as well as drawing inferences from the resulting prediction equations. In addition to evaluating hypotheses about the connections between human activities and biotic responses, we illustrate how the structural equation (SE) model can be queried to understand how interventions might take advantage of an environmental threshold to limit Typha invasions. The guidelines presented provide for an updated definition of the SEM process that subsumes the historical matrix approach under a graph-theory implementation. The implementation is also designed to permit complex specifications and to be compatible with various estimation methods. Finally, they are meant to foster the use of probabilistic reasoning in both retrospective and prospective considerations of the quantitative implications of the results.

We consider rules for discarding predictors in lasso regression and related problems, for computational efficiency. El Ghaoui and his colleagues have proposed 'SAFE' rules, based on univariate inner products between each predictor and the outcome, which guarantee that a coefficient will be 0 in the solution vector. This provides a reduction in the number of variables that need to be entered into the optimization. We propose strong rules that are very simple and yet screen out far more predictors than the SAFE rules. This great practical improvement comes at a price: the strong rules are not foolproof and can mistakenly discard active predictors, i.e. predictors that have non-zero coefficients in the solution. We therefore combine them with simple checks of the Karush-Kuhn-Tucker conditions to ensure that the exact solution to the convex problem is delivered. Of course, any (approximate) screening method can be combined with the Karush-Kuhn-Tucker conditions to ensure the exact solution; the strength of the strong rules lies in the fact that, in practice, they discard a very large number of the inactive predictors and almost never commit mistakes. We also derive conditions under which they are foolproof. Strong rules provide substantial savings in computational time for a variety of statistical optimization problems.

This article attempts to reformulate and resuscitate the seemingly prosaic methodological task of description, which is often derided in favour of causal analysis. First, the problem of definition is addressed: what does this category of analysis (‘description’) refer to? Secondly, a taxonomy of descriptive arguments is offered, emphasizing the diversity contained within this genre of empirical analysis. Thirdly, the demise of description within political science is charted over the past century, with comparisons to other disciplines. Fourthly, it is argued that the task of description ought to be approached independently, not merely as a handmaiden of causal theories. Fifthly, the methodological difficulties of descriptive inference are addressed. Finally, fruitful research areas within the rubric of description are reviewed.

Autism spectrum disorder (ASD) has been reported to exhibit altered local functional consistency. However, previous studies mainly focused on male samples and explored the temporal consistency in the ASD brain ignoring the spatial consistency. In this study, FOur-dimensional Consistency of local neural Activities (FOCA) analysis was used to investigate the sex differences of local spatiotemporal consistency of spontaneous brain activity in ASD. This study used resting-state functional magnetic resonance imaging data from the Autism Brain Imaging Data Exchange database, including 64 males/64 females with ASD and 64 male/64 female neurotypical controls (NCs). Two-way analysis of variance was performed to ascertain diagnosis-by-sex interaction effects on whole brain FOCA maps. Moreover, granger causal analysis was used to investigate effective connectivity between the brain regions with interaction effects and the whole-brain in ASD. Significant diagnosis-by-sex interaction effects on FOCA were observed in the bilateral precuneus (PCUN), bilateral medial prefrontal cortex and right dorsolateral superior frontal gyrus. Specifically, FOCA was significantly increased in males with ASD but decreased in females with ASD in the PCUN compared with the sex-matched NC group. In addition, the lack of sex differences in the causal influences from the bilateral anterior cingulate cortex/medial prefrontal cortex to the PCUN was observed in ASD. Our results reveal altered sex differences in the spatiotemporal consistency of spontaneous brain activity and functional interaction of the anterior and posterior default mode network (DMN) in ASD, highlighting the critical role of the DMN in the sex heterogeneity of ASD.

Atmospheric aridity (vapor pressure deficit, VPD) and soil moisture (SM) deficit limit plant photosynthesis and, thus, affect vegetation carbon uptake. The strong correlation between SM and VPD makes it challenging to delineate their relative contributions to regional vegetation productivity. Addressing this gap is vital to understand the future trajectory of plant productivity in India—the second-highest contributor to global greening. Here, we separate the controls of SM and VPD on the Indian vegetation using statistical and causal analysis. We found that vegetation productivity in India is primarily controlled by SM limitation (87.66% of grids) than VPD limitation (12.34% of grids). Vegetation has a varying association with SM and VPD across different agroecological regions in India. The negative impact of VPD on vegetation carbon uptake is not visible in high-rainfall areas of India. These findings advance our understanding of vegetation dynamics under regional dryness stress and can enhance dynamic vegetation model estimates for India under changing climate scenarios.

The sea-ice cover in the Barents and Kara Seas (BKS) displays pronounced interannual variability. Both atmospheric and oceanic drivers have been found to influence sea-ice variability, but their relative strength and regional importance remain under debate. Here, we use the Liang-Kleeman information flow method to quantify the causal influence of oceanic and atmospheric drivers on the annual sea-ice cover in the BKS in the Community Earth System Model large ensemble and reanalysis. We find that atmospheric drivers dominate in the northern part, ocean heat transport dominates in the central and northeastern part, and local sea-surface temperature dominates in the southern part. Furthermore, the large-scale atmospheric circulation over the Nordic Seas drives ocean heat transport into the Barents Sea, which then influences sea ice. Under future sea-ice retreat, the atmospheric drivers are expected to become more important.