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Probabilistic numerics and uncertainty in computations
Philipp Hennig1, Michael A Osborne2, Mark Girolami3
1Department of Empirical Inference , Max Planck Institute for Intelligent Systems , Tübingen, Germany.
Proceedings. Mathematical, Physical, and Engineering Sciences
|September 9, 2015
Summary
We advocate for probabilistic numerical methods, which quantify calculation uncertainties. These methods offer improved performance and a unified framework for managing errors in scientific computations.
Area of Science:
- Computational Science
- Numerical Analysis
- Scientific Computing
Background:
- Numerical methods are essential in science and industry but suffer from precision loss.
- Managing numerical uncertainty is critical for complex computations in fields like climate science and astrophysics.
- Contemporary challenges necessitate robust methods for handling uncertainty in scientific data.
Purpose of the Study:
- To promote the adoption of probabilistic numerical methods.
- To demonstrate the benefits of interpreting classic numerical methods through a probabilistic lens.
- To introduce new, adaptable probabilistic algorithms with improved empirical performance.
Main Methods:
- Reinterpreting seminal numerical methods as probabilistic inference.
- Developing new probabilistic algorithms adaptable to specific applications.
- Applying probabilistic numerical methods to real-world problems in astrometry and astronomical imaging.
Main Results:
- Probabilistic interpretation reveals new algorithmic possibilities.
- New probabilistic algorithms show improved empirical performance.
- Demonstrated benefits on astrometry and astronomical imaging problems.
Conclusions:
- Probabilistic numerical methods provide a coherent framework for uncertainty quantification.
- These methods enable better diagnosis and control of computational error sources.
- Further research is needed to address open problems in probabilistic numerical algorithms.
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