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Statistical inference on the explained variation of an outcome by a set of covariates is of particular interest in practice. When the covariates are of moderate to high-dimension and the effects are not sparse, several approaches have been…

We investigate through computational simulations with a pore network model the formation of patterns caused by erosion-deposition mechanisms. In this model, the geometry of the pore space changes dynamically as a consequence of the coupling…

Fires and rainfall are major mechanisms that regulate woody and grassy biomasses in savanna ecosystems. Conditions of long-lasting coexistence of trees and grasses have been mainly studied using continuous-time modelling of tree-grass…

Joint modeling of spatially-oriented dependent variables is commonplace in the environmental sciences, where scientists seek to estimate the relationships among a set of environmental outcomes accounting for dependence among these outcomes…

The process of desertification is usually modeled as a first order transition, where a change of an external parameter (e.g. precipitation) leads to a catastrophic bifurcation followed by an ecological regime shift. However, vegetation…

This paper develops a methodology for robust Bayesian inference through the use of disparities. Metrics such as Hellinger distance and negative exponential disparity have a long history in robust estimation in frequentist inference. We…

Multivariate spatial field data are increasingly common and whose modeling typically relies on building cross-covariance functions to describe cross-process relationships. An alternative viewpoint is to model the matrix of spectral…

Statistical modeling of monthly, seasonal, or annual rainfall data is an important research area in meteorology. These models play a crucial role in rainfed agriculture, where a proper assessment of the future availability of rainwater is…

Robustness verification of neural networks, referring to formally proving that neural networks satisfy robustness properties, is of crucial importance in safety-critical applications, where model failures can result in loss of human life or…

Network diffusion models are used to study disease transmission, information spread, technology adoption, and other socio-economic processes. We show that estimates of these diffusions are highly non-robust to mismeasurement. First, even…

Deep sequence models are receiving significant interest in current machine learning research. By representing probability distributions that are fit to data using maximum likelihood estimation, such models can model data on general…

Spatially dependent parameters of a two-component chaotic reaction-diffusion PDE model describing ocean ecology are observed by sampling a single species. We estimate model parameters and the other species in the system by…

Robust pedestrian trajectory forecasting is crucial to developing safe autonomous vehicles. Although previous works have studied adversarial robustness in the context of trajectory forecasting, some significant issues remain unaddressed. In…

Landscapes are meaningful ecological units that strongly depend on the environmental conditions. Such dependencies between landscapes and the environment have been noted since the beginning of Earth sciences and cast into conceptual models…

Drought is a serious natural disaster that has a long duration and a wide range of influence. To decrease the drought-caused losses, drought prediction is the basis of making the corresponding drought prevention and disaster reduction…

Weather and climate forecasts are inherently uncertain due to chaotic dynamics, imperfect initial conditions, and incomplete representation of the underlying physical processes. Operational ensemble forecasts aim to represent these…

Two canonical problems in geostatistics are estimating the parameters in a specified family of stochastic process models and predicting the process at new locations. A number of asymptotic results addressing these problems over a fixed…

A wide body of work has applied the concept of critical slowing down to estimate the stability of different Earth system components. Most of them -- such as global vegetation -- are inherently non-stationary, for example due to strong…

This thesis focuses on the applications of mathematical tools and concepts brought from nonequilibrium statistical physics to the modeling of ecological problems. The first part provides a short introduction where the theoretical concepts…

Mining frequent patterns is plagued by the problem of pattern explosion making pattern reduction techniques a key challenge in pattern mining. In this paper we propose a novel theoretical framework for pattern reduction. We do this by…