More than 100 researchers from across the country attended the opening workshop for the Program on Model Uncertainty: Mathematical and Statistical (MUMS) on the campus of Duke University in late August.
The MUMS program brings together statisticians and applied mathematicians with disciplinary scientists from a wide-range of fields to understand the effects of modeling and uncertainty on predictions. The focus of the workshop was to layout the foundations for the MUMS program by examining the theoretical basis for statistical uncertainty, the strengths and weaknesses of models of real world processes and the uncertainty of those processes.
The workshop featured statisticians, mathematicians and data science researchers who presented their talks on how model uncertainty and uncertainty quantification methodologies can be used across a broad spectrum of subjects.
“The kickoff meeting brought together the world leaders in uncertainty quantification, many of
whom continue to work and interact at SAMSI as long-term visitors,” said David Banks, Director of SAMSI and the program’s directorate liaison. “Additionally, the participants are teaching a graduate course in model uncertainty, which has drawn in students from all over the Triangle.”
In addition to the working groups, a fall course is being presented for graduate students that introduces statistical and mathematical sensitivity analysis and uncertainty quantification techniques for large-scale models arising in current applications. The course is ongoing through December.
“The MUMS program is a classic melding of applied mathematics and statistics,” said Banks.
“Uncertainty quantification is an exciting new field, with important applications in weather forecasting, modeling of pyroclastic flows, and materials science, among others.”
The opening workshop produced six working groups:
- Uncertainty Quantification in Materials
- Reduced Order Models (ROMS) Theory and Application
- Prediction Uncertainty and Extrapolation
- Data Fusion
- Foundations of Model Uncertainty
The working groups will meet throughout the academic year and discuss ways to use these uncertainty principles in a diverse variety of disciplines, such as: engineering, probability, operations research and machine learning, just to name a few.
“One of the grand challenges scientists face is how to make probability statements when the model is so complex and intractable that it cannot be studied with standard tools from mathematical statistics,” said Banks. “The MUMS program provides a general solution strategy, by approximating the complex model with Gaussian processes. Bayesian methods enable the scientist to not only fit the most accurate Gaussian process, but also to estimate a discrepancy function, which indicates where the approximation is poor.”
For more information about the MUMS program, visit: https://www.samsi.info/mums.