Fusion learning for inter-laboratory comparisons

In this paper we propose a Generalized Fiducial Inference inspired method for finding a robust consensus of several independently derived collection of confidence distributions (CDs) for a quantity of interest. The resulting fused CD is robust to the existence of potentially discrepant CDs in the collection. The method uses computationally efficient fiducial model averaging to obtain a robust consensus distribution without the need to eliminate discrepant CDs from the analysis. This work is motivated by a commonly occurring problem in inter-laboratory trials, where different national laboratories all measure the same unknown true value of a quantity and report their CDs. These CDs need to be fused to obtain a consensus CD for the quantity of interest. When some of the CDs appear to be discrepant, simply eliminating them from the analysis is often not an acceptable approach, particularly so in view of the fact that the true value being measured is not known and a discrepant result from a lab may be closer to the true value than the rest of the results. Additionally, eliminating one or more labs from the analysis can lead to political complications since all labs are regarded as equally competent. These considerations make the proposed method well suited for the task since no laboratory is explicitly eliminated from consideration. We report results of three simulation experiments showing that the proposed fiducial approach has better small sample properties than the currently used naive approaches. Finally, we apply the proposed method to obtain consensus CDs for gauge block calibration inter-laboratory trials and measurements of Newton's constant of gravitation (G) by several laboratories.