Visualizing discrepancies from nonlinear models and computer experiments. (24th July 2015)

• Record Type: Journal Article
• Authors: Weaver, Brian P.; Warr, Richard L.; Anderson‐Cook, Christine M.; Higdon, David M.
• Is Part Of: Statistical analysis and data mining. Volume 8:Number 5/6(2015)
• Page Start: 274
• Page End: 286
• Publication Date: 2015-07-24
• Subjects: Gaussian process -- Plutonium‐238 -- Calibration -- Science‐based model; Data mining -- Statistical methods -- Periodicals; 006.312
• DOI: 10.1002/sam.11282
• Languages: English
• ISSNs: 1932-1864

Abstract

Abstract: Plutonium‐238 is an important specialized power source that radiates heat, which can be converted into electricity. This case study models the thermal output of samples of Pu‐238, in which the underlying theoretical model of its decay summarizes a large portion of the observed behavior. A discrepancy function is used to account for missing structure seen in the observed data, but is not included in the physical model. The model combines the assumed physics model, discrepancy and experimental error with an expression of the form, f ( x, θ ) + δ ( x ) + ɛ . The combined model improves prediction of new observations in the future by accounting for shortcomings or omissions in the physical model and provides quantitative summaries of the relative contributions of the discrepancy and physics model. In this work, we illustrate how to visualize the discrepancy function when it is modeled using a Gaussian process. With the visualization, scientists can gain understanding about the differences between the observed data and the current scientific model and develop proposals of how to potentially improve their model. A secondary example illustrates how the visualization methods can help with understanding in higher dimensions.