Jim Berger, Don Estep, and Max Gunzburger
The ASA and Society for Industrial and Applied Mathematics (SIAM) recently recognized the needed synergy between mathematics and statistics to address major challenges at the interface of computer modeling of complex processes and data by embarking on a joint effort to create the Journal on Uncertainty Quantification (JUQ). The journal will be published by SIAM and initially led by the editorial team of Jim Berger, representing the ASA, and Don Estep and Max Gunzburger, representing SIAM.
In broad terms, uncertainty quantification (UQ) in computational science and engineering has to do with describing the effects of error and uncertainty on results based on simulation and prediction of the behavior of constructed models of phenomena in physics, biology, chemistry, ecology, engineered systems, politics, etc. That the subject is labeled uncertainty quantification outside of statistics leads to confusion because statisticians typically use the phrase for any aspect of statistics for which an accuracy assessment is attached; UQ herein is reserved for the more limited definition, reflecting the scope of the journal.
Results from mathematical modeling are subject to errors and uncertainty emanating from a variety of sources, including uncertainty in data obtained from experiment and observation; limitations of physical modeling, including uncertain coefficients, approximation, and the need for emulation; problems in computer codes; and the difficulty of combining models into integrated systems. Of course, many of the same issues arise in understanding the uncertainties associated with any simulation model (such as agent-based models) and complex statistical models. Quantifying the effects of these uncertainties is crucial to accurately modeling and predicting real complex processes through computational simulators.
In specific terms, UQ embraces a number of problems, including:
- Code verification
- Model validation and estimating structural model error
- Computational error estimation for numerical solutions (e.g., a posterior error analysis)
- Data assimilation and model calibration
- Detection and forecasting of high-impact, rare events
- Emulation of computer models and dimension reduction
- Inference with complex multiscale, multiphysics models
- Representation of uncertainty and error and integration of different types of uncertainty (e.g., parameter uncertainty, numerical error, and structural model error)
- Inverse problems, decisionmaking, and optimization under uncertainty
- Treatment of high-dimensional spaces
Addressing such problems requires tackling mathematical and statistical research of great technical difficulty. General mathematical components of UQ include probability, measure theory, functional analysis, differential equations, graph and network theory, approximation theory, and ergodic theory. At the same time, nearly all aspects of the statistical sciences are relevant to UQ. Moreover, much of this research is necessarily carried out in interdisciplinary settings.
JUQ will contain research articles presenting significant mathematical, statistical, algorithmic, and application advances in UQ in the context of simulation, prediction, control, and optimization in science and engineering and related fields such as sensitivity analysis, model validation, model calibration, data assimilation, and code verification. A key goal of JUQ will be nurturing synergistic interactions between the mathematical, statistical, computational, and applications communities involved in uncertainty quantification and related areas. To this end, JUQ solicits papers describing new ideas that could lead to significant progress in methodology, computational/algorithmic aspects, and fully conceived applications of uncertainty quantification, as well as review articles on particular aspects.
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