Combining inconsistent data

At present, the most widely used procedure for finding the value of a quantity from data obtained by different observers involves calculating the inverse-variance weighted mean of the observers' estimates. This method produces reasonable results if the data are consistent. However, in many cases a consistency test reveals the possible existence of outliers that nevertheless have to be included in the evaluation task. In this paper the Bayesian understanding of probability is used to treat this problem. It is first shown that the weighted mean method results from the assumption that the observers' biases are identically zero. If the data do not support this assumption, other evaluation methods are needed. Three such methods are then derived, application of which is discussed through a simulated example.