Combination of measurements and the BLUE method

The most accurate method to combine measurement from different experiments is to build a combined likelihood function and use it to perform the desired inference. This is not always possible for various reasons, hence approximate methods are often convenient. Among those, the best linear unbiased estimator (BLUE) is the most popular, allowing to take into account individual uncertainties and their correlations. The method is unbiased by construction if the true uncertainties and their correlations are known, but it may exhibit a bias if uncertainty estimates are used in place of the true ones, in particular if those estimated uncertainties depend on measured values. In those cases, an iterative application of the BLUE method may reduce the bias of the combined measurement.