Dealing with prior knowledge about the measurand

Abstract

Suppose a measurand can be computed by two different but consistent measurement models. Then, the output of one of the models would serve as prior knowledge to the other. In this paper, two alternative methods to produce a PDF for the measurand that take into account both models are presented.

The first method proceeds by propagating the PDFs for the input quantities through the corresponding models in the usual way and then merging the resulting PDFs using the logarithmic or linear pooling techniques. The result is a kind of ‘compromise distribution’ of the pooled PDFs.

The second method starts by propagating the PDFs for all input quantities except one, say X1, through the model that relates the former quantities to the latter. In this way the PDF for X1 is obtained, which is then updated using its likelihood. The resulting PDF, which encodes all information available, is finally propagated through the model that relates X1 to the measurand. This second method is the preferred way of analysis, because it results in a PDF that is narrower than the one obtained with the first method.