Mathematical frameworks for analyzing data and uncertainty, including statistical inference, Bayesian methods, risk analysis, stochastic processes, and decision-making under uncertainty
5 papersThis book explores the "statistical consequences of fat tails", demonstrating that standard statistical methods break down in the presence of extreme events. It provides a range of adjustments, heuristics, and commentary for both statistical inference and decision-making under such conditions.
Modern science has experienced overall exponential growth with a doubling time of 17.3 years, but this growth is not uniform. Distinct periods of varying growth rates correlate with economic and political developments, such as industrialization and world wars, showcasing the interplay between science and society. Analysis of growth rates in the UK versus worldwide, and in life sciences versus physical and technical sciences, revealed relatively comparable trends.
Sensitivity analysis is becoming an essential tool for systems modeling and policy support, but its full potential is yet to be realized. The paper identifies key challenges and opportunities, including structuring sensitivity analysis as a discipline, addressing computational burdens, integrating with machine learning, and clarifying its relationship with uncertainty quantification and decision-making.
This paper proposes a modular framework for active learning reliability analysis and benchmarks 39 different strategies on 20 reliability problems. The study finds that PC-Kriging combined with subset simulation, the deviation number U learning function, and a combined stopping criterion generally performs best, although no single strategy is universally superior (no free lunch!). Over-calibrating reliability solvers when using surrogate models is shown to improve accuracy.
The paper defines digital twins as models coupled with evolving data and an updating mechanism, emphasizing their value for representing changing objects. It discusses various potential applications of digital twins in manufacturing, medicine, and fundamental science, highlighting the importance of model validation, uncertainty evaluation, and data reduction techniques.