Application of Bayesian model averaging to the determination of thermal expansion of single-crystal silicon. (14th March 2019)

• Record Type: Journal Article
• Authors: Martin, Jörg; Bartl, Guido; Elster, Clemens
• Is Part Of: Measurement science & technology. Volume 30:Number 4(2019:Apr.)
• Publication Date: 2019-03-14
• Subjects: Bayesian model averaging -- coefficient of thermal expansion -- Einstein term -- model comparison -- model uncertainty -- derivative -- g-prior; Physical measurements -- Periodicals; Scientific apparatus and instruments -- Periodicals; Equipment and Supplies -- Periodicals; Science -- instrumentation -- Periodicals; Technology -- instrumentation -- Periodicals; Mesures physiques -- Périodiques; Physical measurements; Scientific apparatus and instruments; Periodicals; 502.87
• DOI: 10.1088/1361-6501/ab094b
• Languages: English
• ISSNs: 0957-0233

Abstract

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.