The compositional meaning of the dection limit

In compositional data analysis a value below detection limit (BDL) is typically modeled as the definitive information that the actual value is below some fixed value - the detection limit (see e.g. Palarea-Albaladejo et. al (2007, 2008)). Analytical chemistry (Heinrichs and Herrmann (1990); Fletcher (1981); Kellner et al. (2004)) however has a different view on measured concentrations. The measured concentration Cm is not the true concentration cm of the measurant but a quantity computed from an observable quantity Om through a calibration equation. This has serious consequences for the interpretation and statistical analysis of below detection limit observations in the context of compositional data analysis.