Fusion learning for Interlaboratory Comparison

In this paper we propose a Generalized Fiducial Inference inspired m ethod for finding a robust consensus of several independently derived collection of confiden ce distributions (CDs) for a quantity of interest. The resulting fused CD is robust to the existence of pote ntially discrepant CDs in the collec- tion. The method uses computationally efficient fiducial model avera ging to obtain a robust consensus distribution without the need to eliminate discrepant CDs from the an alysis. This work is motivated by a commonly occurring problem in interlaboratory trials, where diffe rent national laboratories all measure same unknown true value of a quantity and report their CD s. These CDs need to be fused to obtain a consensus CD for the quantity of interest. When some of t he CDs appear to be discrepant, simply eliminating them from the analysis is often not an acceptable app roach, 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, e liminating one or more labs from the analysis can lead to political complications since all labs are regard ed as equally competent. These considerations make the proposed method well suited for the task since no laboratory is explicitly elimi- nated from consideration. We report results of three simulation ex periments showing that the proposed fiducial approach has better small sample properties than the cur rently used naive approaches. Finally, we apply the proposed method to obtain consensus CDs for gauge b lock calibration interlaboratory trials and measurements of Newton’s constant of gravitation ( G ) by several laboratories.