This course provides a brief survey of mathematical methods for uncertainty quantification. It highlights various issues, techniques and practical tools available for modeling uncertainty in quantitative models of complex dynamic systems. Specific topics include basic concepts in probability and statistics, spatial statistics (geostatistics and machine learning), Monte Carlo simulations, global and local sensitivity analyses, surrogate models, and computational alternatives to Monte Carlo simulations (e.g., quasi-MC, moment equations, the method of distributions, polynomial chaos expansions). Prerequisites: algebra (CME 104 or equivalent), introductory statistics course (CME 106 or equivalent).
3 units · Letter or Credit/No Credit
This course provides a brief survey of mathematical methods for uncertainty quantification. It highlights various issues, techniques and practical tools available for modeling uncertainty in quantitative models of complex dynamic systems. Specific topics include basic concepts in probability and statistics, spatial statistics (geostatistics and machine learning), Monte Carlo simulations, global and local sensitivity analyses, surrogate models, and computational alternatives to Monte Carlo simulations (e.g., quasi-MC, moment equations, the method of distributions, polynomial chaos expansions). Prerequisites: algebra (CME 104 or equivalent), introductory statistics course (CME 106 or equivalent).
Offered in Spring 2027 at Stanford University.