Combining data sets in data analysis with interval uncertainty

A practical example of the use of interval statistics methods in the field of nuclear physics is given. It is shown how these methods allow combining two samples in an optimal way. The correction parameter of one of the samples is a multiplicative correction for the background in one of the spectral regions. From physical considerations, the background value estimate is known. The working tool in optimization is a combined measure of consistency, which ensures the receipt of external and internal estimates simultaneously. Optimality in this case implies an increase in the size of the maximum clique in the interval sample. Thus, the volume of data for calculating the constant of the fundamental nuclear reaction increases, which makes the calculation result more reliable. Based on the results of combining the samples, a new value of the physical quantity was calculated, namely, the circular polarization of gamma quanta in the reaction of capture of a polarized neutron by protons.