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Forecasting techniques for assessing the power of future experiments to discriminate between theories or discover new laws of nature are of great interest in many areas of science. In this paper, we introduce a Bayesian forecasting method…
Extreme El Ni\~no events, such as occurred in 1997--1998, can induce severe weather on a global scale, with significant socioeconomic impacts that motivate efforts to understand them better. However, extreme El Ni\~no events are rare, and…
In recent years, the climate change research community has become highly interested in describing the anthropogenic influence on extreme weather events, commonly termed "event attribution." Limitations in the observational record and in…
In context-specific applications such as robotics, telecommunications, and healthcare, artificial intelligence systems often face the challenge of limited training data. This scarcity introduces epistemic uncertainty, i.e., reducible…
To address the uncertainty in outputs of numerical weather prediction (NWP) models, ensembles of forecasts are used. To obtain such an ensemble of forecasts the NWP model is run multiple times, each time with different formulations and/or…
While numerical weather prediction (NWP) models are essential for forecasting thunderstorms hours in advance, NWP uncertainty, which increases with lead time, limits the predictability of thunderstorm occurrence. This study investigates how…
Language prediction is constrained by informational entropy intrinsic to language, such that there exists a limit to how accurate any language model can become and equivalently a lower bound to language compression. The most efficient…
Forecasting accuracy is bounded by the information available about the future. This paper makes that statement precise using information-theoretic tools. Under logarithmic loss, the expected performance of any probabilistic forecast…
Sequential recommender systems have achieved steady gains in offline accuracy, yet it remains unclear how close current models are to the intrinsic accuracy limit imposed by the data. A reliable, model-agnostic estimate of this ceiling…
Uncertainty in return level estimates for rare events, like the intensity of large rainfall events, makes it difficult to develop strategies to mitigate related hazards, like flooding. Latent spatial extremes models reduce uncertainty by…
Entropy governs molecular self-assembly, phase transitions, and material stability, yet remains challenging to quantify and directly control in molecular systems. Here, we demonstrate that the computable information density (CID), a data…
Here we define natural chaotic systems, like the earths weather and climate system, as chaotic systems which are open to the world so have constantly changing boundary conditions, and measurements of their states are subject to errors. In…
Although some information-theoretic measures of uncertainty or granularity have been proposed in rough set theory, these measures are only dependent on the underlying partition and the cardinality of the universe, independent of the lower…
The Principle of Maximum Entropy is a rigorous technique for estimating an unknown distribution given partial information while simultaneously minimizing bias. However, an important requirement for applying the principle is that the…
The information entropy of a nuclear density distribution is calculated for a number of nuclei. Various phenomenological models for the density distribution using different geometry are employed. Nuclear densities calculated within various…
Thermal conditions in the urban canopy exhibit stochastic variability driven by varied radiative fluxes and turbulent wind fields, requiring probabilistic rather than deterministic prediction methods. This study presents a probabilistic…
El Ni\~no-Southern Oscillation (ENSO) exhibits significant impacts on the frequency of extreme weather events and its socio-economic implications prevail on a global scale. However, a fundamental gap still exists in understanding the…
Eliciting information to reduce uncertainty about a latent entity is a critical task in many application domains, e.g., assessing individual student learning outcomes, diagnosing underlying diseases, or learning user preferences. Though…
Predictive statistical mechanics is a form of inference from available data, without additional assumptions, for predicting reproducible phenomena. By applying it to systems with Hamiltonian dynamics, a problem of predicting the macroscopic…
Tropical cyclones (TCs) rank among the most costly natural disasters in the United States, and accurate forecasts of track and intensity are critical for emergency response. Intensity guidance has improved steadily but slowly, as processes…