Biases in Weighted Estimation Methods

In the Gaia archive, certain numerical values of the same estimated quantities vary significantly from one table to another. One such example is one of the simplest estimators: the mean magnitude. In Gaia, and more generally in astronomy, we often encounter uncertainties that vary from one measurement to another. This phenomenon is known as heteroscedasticity. In such situations, it is customary to employ weighted procedures. However, here we show that in certain cases weighted procedures can lead to biased estimations. These biases typically arise from the lack of independence between the measurement and its uncertainty, or because the uncertainties are complex to estimate precisely. Also affecting the estimation of the mean magnitude is the non-linear transformation between flux and magnitudes and how to deal with negative fluxes.

The moral of the tale: even the estimation of the mean can present tricky complications.

EAS2024, European Astronomical Society Annual Meeting