Application of Bayesian model averaging to the determination of thermal expansion of single-crystal silicon

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 283K-305K 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.