Model uncertainty can become a critical issue in the presence of several plausible models. Due to its definition by a derivative the coefficient of thermal expansion is quite vulnerable when… Click to show full abstract
Model uncertainty can become a critical issue in the presence of several plausible models. Due to its definition by a derivative the coefficient of thermal expansion is quite vulnerable when it comes to model choice. Using length measurements of single-crystal silicon in the temperature range we study the results of a physical model and a polynomial model. While we have consistency of the length fits we observe a noticeable difference for the derived coefficient of thermal expansion between these models. We here propose a method based on Bayesian model averaging to account for model uncertainty in such situations which provides coherent estimates with more realistic uncertainties. In addition, it yields a posteriori model probabilities that indicate, for our data, a slight preference for the physical model. Our approach is widely applicable to cases where badly behaved operations such as derivatives make model uncertainty an inevitable task.
               
Click one of the above tabs to view related content.