Model Uncertainty: Conservative Propagation Through Polynomial Regressions with Unknown Structure

• Activity Number: 114 - The Need and Methods for Routine Inclusion of Model Uncertainty in Statistical Results
• Type: Topic Contributed
• Date/Time: Monday, July 31, 2017 : 8:30 AM to 10:20 PM
• Sponsor: Quality and Productivity Section
• Author(s): Scott Ferson*
• Companies: Insitute for Risk and Uncertainty, University of Liverpool
• Keywords: model uncertainty ; polynomial regression ; risk analysis ; propagation of uncertainty ; polynomial order

Abstract

How can we project uncertainty about X through a function to characterize the uncertainty about its output Y when the function itself has not been precisely characterized? We describe some special cases where this problem has been solved comprehensively, and consider a new case with polynomial functions. When evidence of a relationship between variables has been condensed into regression analyses, a simple convolution using regression statistics allows us to reconstruct the scatter of points processed in the original regression model, but regression analysis does not necessarily select a model that actually reflects how data were generated. What if we do not know which order polynomial should have been used in the regression analysis? We describe a simple and inexpensive projection approach that yields conservative characterizations no matter what polynomial actually generated the data. The result represents the uncertainty induced in Y owing to the underlying uncertainty about X, and the model uncertainty about which degree polynomial is correct, contingent on the presumption that a polynomial model of some order is appropriate. The results appear to be useful for risk analysis.