We commonly refer to state estimation theory in geosciences as data assimilation (DA). This
term encompasses the entire sequence of operations that, starting from the observations of a …

Particle filters contain the promise of fully nonlinear data assimilation. They have been
applied in numerous science areas, including the geosciences, but their application to high …

Selecting a suitable pretraining dataset is crucial for both general-domain (eg, GPT-3) and
domain-specific (eg, Codex) language models (LMs). We formalize this problem as selecting …

Estimation of the prevalence and contagiousness of undocumented novel coronavirus
[severe acute respiratory syndrome–coronavirus 2 (SARS-CoV-2)] infections is critical for …

This open-access textbook's significant contribution is the unified derivation of data-
assimilation techniques from a common fundamental and optimal starting point, namely …

A central research challenge for the mathematical sciences in the twenty-first century is the
development of principled methodologies for the seamless integration of (often vast) data …

The subject of inverse problems in differential equations is of enormous practical
importance, and has also generated substantial mathematical and computational …

This book places data assimilation (DA) into the broader context of inverse problems and the
theory, methods, and algorithms that are used for their solution. It strives to provide a …

This tutorial paper reviews the use of advanced Monte Carlo sampling methods in the
context of Bayesian model updating for engineering applications. Markov Chain Monte …

Influenza recurs seasonally in temperate regions of the world; however, our ability to predict
the timing, duration, and magnitude of local seasonal outbreaks of influenza remains limited …