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Autoregressive models are ubiquitous tools for the analysis of time series in many domains such as computational neuroscience and biomedical engineering. In these domains, data is, for example, collected from measurements of brain activity.…

The evolution of states of a spatial ecological model is studied. The model describes an infinite population of point entities placed in $\mathbb{R}^d$ which reproduce themselves at distant points (disperse) and die with rate that includes…

We propose a multiscale approach for predicting quantities in dynamical systems which is explicitly structured to extract information in both fine-to-coarse and coarse-to-fine directions. We envision this method being generally applicable…

Complex systems are characterized by a huge number of degrees of freedom often interacting in a non-linear manner. In many cases macroscopic states, however, can be characterized by a small number of order parameters that obey stochastic…

Regression methods dominate the practice of biostatistical analysis, but biostatistical training emphasises the details of regression models and methods ahead of the purposes for which such modelling might be useful. More broadly,…

Nonlinear machine-learning models are increasingly used to discover causal relationships in time-series data, yet the interpretation of their outputs remains poorly understood. In particular, causal scores produced by regularized neural…

Over the last few decades, ecologists have come to appreciate that key ecological patterns, which describe ecological communities at relatively large spatial scales, are not only scale dependent, but also intimately intertwined. The…

Foundation models pretrained on diverse data at scale have demonstrated extraordinary capabilities in a wide range of vision and language tasks. When such models are deployed in real world environments, they inevitably interface with other…

A majority of recent advancements related to the fault diagnosis of electrical motors are based on the assumption that training and testing data are drawn from the same distribution. However, the data distribution can vary across different…

There has been active investigation into deep learning approaches for time series analysis, including foundation models. However, most studies do not address significant scientific applications. This paper aims to identify key features in…

Much of scientific data is collected as randomized experiments intervening on some and observing other variables of interest. Quite often, a given phenomenon is investigated in several studies, and different sets of variables are involved…

Advances in GPS telemetry technology have enabled analysis of animal movement in open areas. Ecologists today are utilizing modern analytic tools to study animal behaviors from large quantity of GPS coordinates. Analytic tools with…

Biological systems display impressive capabilities in effectively responding to environmental signals in real time. There is increasing evidence that organisms may indeed be employing near optimal Bayesian calculations in their…

One of the main tasks of actuaries and data scientists is to build good predictive models for certain phenomena such as the claim size or the number of claims in insurance. These models ideally exploit given feature information to enhance…

The recent development of foundation models for time series data has generated considerable interest in using such models across a variety of applications. Although foundation models achieve state-of-the-art predictive performance, their…

This paper develops a new framework, called modular regression, to utilize auxiliary information -- such as variables other than the original features or additional data sets -- in the training process of linear models. At a high level, our…

Discovering causal relationship using multivariate functional data has received a significant amount of attention very recently. In this article, we introduce a functional linear structural equation model for causal structure learning when…

Large foundation models (FMs) are transforming Earth science by integrating heterogeneous multimodal data, such as multi-platform imagery, gridded reanalysis data, diverse geophysical and geochemical observations, and domain-specific text,…

We present an AI-based ecosystem simulator that uses three-dimensional models of the terrain and animal models controlled by deep reinforcement learning. The simulations take place in a game engine environment, which enables continuous…

The classical regular and partial autocorrelation functions are powerful tools for stationary time series modelling and analysis. However, it is increasingly recognized that many time series are not stationary and the use of classical…