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This article investigates the causality structure of financial time series. We concentrate on three main approaches to measuring causality: linear Granger causality, kernel generalisations of Granger causality (based on ridge regression and…

Quantifying the impacts of anthropogenic global warming requires accurate Earth system model (ESM) simulations. Statistical bias correction and downscaling can be applied to reduce errors and increase the resolution of ESMs. However,…

Pollinators play a crucial role for plant reproduction, either in natural ecosystem or in human-modified landscape. Global change drivers,including climate change or land use modifications, can alter the plant-pollinator interactions. To…

Wahl et al. (2016, 2017) introduced the idea of Granger causality (GC) maps for Langevin systems: dynamics are localised linearly at each point in phase space as vector Ornstein-Uhlenbeck (VOU) processes, for which GCs may in principle be…

Granger causality has become an indispensable tool for analyzing causal relationships between time series. In this paper, we provide a detailed overview of its mathematical foundations, trace its historical development, and explore how…

Learning Granger causality for general point processes is a very challenging task. In this paper, we propose an effective method, learning Granger causality, for a special but significant type of point processes --- Hawkes process. We…

Measuring and monitoring soil organic carbon is critical for agricultural productivity and for addressing critical environmental problems. Soil organic carbon not only enriches nutrition in soil, but also has a gamut of co-benefits such as…

Vegetation often understood merely as the result of long-term climate conditions. However, vegetation itself plays a fundamental role in shaping Earth's climate by regulating the energy, water, and biogeochemical cycles across terrestrial…

In recent decades, the causes and consequences of climate change have accelerated, affecting our planet on an unprecedented scale. This change is closely tied to the ways in which humans alter their surroundings. As our actions continue to…

Wildfire forecasting is notoriously hard due to the complex interplay of different factors such as weather conditions, vegetation types and human activities. Deep learning models show promise in dealing with this complexity by learning…

This survey paper covers the breadth and depth of time-series and spatiotemporal causality methods, and their applications in Earth Science. More specifically, the paper presents an overview of causal discovery and causal inference,…

This paper introduces warped Gaussian processes (WGP) regression in remote sensing applications. WGP models output observations as a parametric nonlinear transformation of a GP. The parameters of such prior model are then learned via…

We study causality between bivariate curve time series using the Granger causality generalized measures of correlation. With this measure, we can investigate which curve time series Granger-causes the other; in turn, it helps determine the…

Multivariate time series anomaly detection has numerous real-world applications and is being extensively studied. Modeling pairwise correlations between variables is crucial. Existing methods employ learnable graph structures and graph…

Granger causality is a statistical notion of causal influence based on prediction via vector autoregression. Developed originally in the field of econometrics, it has since found application in a broader arena, particularly in neuroscience.…

Climate models encapsulate our best understanding of the Earth system, allowing research to be conducted on its future under alternative assumptions of how human-driven climate forces are going to evolve. An important application of climate…

The Gaussian process (GP) is a widely used probabilistic machine learning method with implicit uncertainty characterization for stochastic function approximation, stochastic modeling, and analyzing real-world measurements of nonlinear…

Granger causal modeling is an emerging topic that can uncover Granger causal relationship behind multivariate time series data. In many real-world systems, it is common to encounter a large amount of multivariate time series data collected…

The scientific rigor and computational methods of causal inference have had great impacts on many disciplines, but have only recently begun to take hold in spatial applications. Spatial casual inference poses analytic challenges due to…

Prior beliefs about the latent function to shape inductive biases can be incorporated into a Gaussian Process (GP) via the kernel. However, beyond kernel choices, the decision-making process of GP models remains poorly understood. In this…