Comparison of Statistic and Deterministic Frameworks of Uncertainty Quantification

16 maio 2015, 10:51 • Maria do Rosário De Oliveira Silva

Rui Paulo

(ISEG and CEMAPRE, Universidade de Lisboa)

 

21 May 2015 (Thursday), 11:30

 

Room P3.10

(Math. Building, IST, Av. Rovisco Pais, 1049-001 Lisboa)

 

Two different approaches to the prediction problem are compared employing a realistic example, combustion of natural gas, with 102 uncertain parameters and 76 quantities of interests. One approach, termed Bound-to-Bound Data Collaboration (abbreviated to B2B) deploys semi-definite programming algorithms where the initial bounds on unknowns are combined with the initial bound of experimental data to produce new uncertainty bounds for the unknowns that are consistent with the data and, finally, deterministic uncertainty bounds for prediction in new settings. The other approach is statistical and Bayesian, referred to as BCP (for Bayesian Calibration and Prediction). It places prior distributions on the unknown parameters and on the parameters of the measurement error distributions and produces posterior distributions for model parameters and posterior distributions for model predictions in new settings.  The predictions from the two approaches are consistent:  B2B bounds and the support of the BCP predictive distribution overlap a very large part of each other. The BCP predictive distribution is more nuanced than the B2B bounds but depends on stronger assumptions. Interpretation and comparison of the results is closely connected with assumptions made about the model and experimental data and how they are used in both settings. The principal conclusion is that use of both methods protects against possible violations of assumptions in the BCP approach and conservative specifications and predictions using B2B.

Joint work with Michael Frenklach, Andrew Packard (UC Berkeley), Jerome Sacks (National Institute of Statistical Sciences) and Gonzalo Garcia-Donato (Universidad de Castilla-La Mancha)