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Model waveforms are used in gravitational wave data analysis to detect and then to measure the properties of a source by matching the model waveforms to the signal from a detector. This paper derives accuracy standards for model waveforms…

Recent advances in learning techniques have enabled the modelling of dynamical systems for scientific and engineering applications directly from data. However, in many contexts explicit data collection is expensive and learning algorithms…

The last decades have seen an unprecedented increase in the availability of data sets that are inherently global and temporally evolving, from remotely sensed networks to climate model ensembles. This paper provides a view of statistical…

Many applications collect a large number of time series, for example, the financial data of companies quoted in a stock exchange, the health care data of all patients that visit the emergency room of a hospital, or the temperature sequences…

Graph-structured data is a type of data to be obtained associated with a graph structure where vertices and edges describe some kind of data correlation. This paper proposes a regression method on graph-structured data, which is based on…

Stochastic processes are proposed whose master equations coincide with classical wave, telegraph, and Klein-Gordon equations. Similar to predecessors based on the Goldstein-Kac telegraph process, the model describes the motion of particles…

We present a method to estimate two-dimensional, time-invariant oceanic flow fields based on data from both ensemble forecasts and online measurements. Our method produces a realistic estimate in a computationally efficient manner suitable…

Statistical models are an essential tool to model, forecast and understand the hydrological processes in watersheds. In particular, the understanding of time lags associated with the delay between rainfall occurrence and subsequent changes…

We consider the wave equation with highly oscillatory initial data, where there is uncertainty in the wave speed, initial phase and/or initial amplitude. To estimate quantities of interest related to the solution and their statistics, we…

Models of gravitational waveforms play a critical role in detecting and characterizing the gravitational waves (GWs) from compact binary coalescences. Waveforms from numerical relativity (NR), while highly accurate, are too computationally…

While diffusion models can successfully generate data and make predictions, they are predominantly designed for static images. We propose an approach for efficiently training diffusion models for probabilistic spatiotemporal forecasting,…

Classical assessments of trends in gridded temperature data perform independent evaluations across the grid, thus, ignoring spatial correlations in the trend estimates. In particular, this affects assessments of trend significance as…

Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…

A problem of current interest is the estimation of spatially distributed processes at locations where measurements are missing. Linear interpolation methods rely on the Gaussian assumption, which is often unrealistic in practice, or…

Rapid developments in streaming data technologies have enabled real-time monitoring of human activity that can deliver high-resolution data on health variables over trajectories or paths carved out by subjects as they conduct their daily…

Short-range forecasts of precipitation fields are needed in a wealth of agricultural, hydrological, ecological and other applications. Forecasts from numerical weather prediction models are often biased and do not provide uncertainty…

A space-time model for wind fields is proposed. It aims at simulating realistic wind conditions with a focus on reproducing the space-time motions of the meteorological systems. A Gaussian linear state-space model is used where the latent…

Variability in sea ice conditions, combined with strong couplings to the atmosphere and the ocean, lead to a broad range of complex sea ice dynamics. More in-situ measurements are needed to better identify the phenomena and mechanisms that…

We develop Bayesian machine learning methods for mixed data sampling (MIDAS) regressions. This involves handling frequency mismatches and specifying functional relationships between many predictors and the dependent variable. We use…

Graph neural networks have emerged as a powerful tool for learning spatiotemporal interactions. However, conventional approaches often rely on predefined graphs, which may obscure the precise relationships being modeled. Additionally,…