The uncertainty described in the previous section are related to the so-called random, or statistical errors. Other important sources are, generally speaking (see ISO 1993 for details), related to uncertain values of influence variables on which the observed values, or the data-analysis process, might depend. In physics, we usually refer to these as systematic effects or errors. They can be related to the parameters of the experiment, like a particle beam energy or the exposure time, or to environmental variables, like temperature and pressure, calibration constants of the detector, and all other parameters, `constants' (in the physical sense), and hypotheses that enter the data analysis. The important thing is that we are unsure about their precise value. Let us indicate all the influence variables with the vector , and their joint pdf as .
The treatment of uncertainties due to systematic errors has traditionally been lacking a consistent theory, essentially due the unsuitability to standard statistical methods of dealing with uncertainty in the most wide sense. Bayesian reasoning becomes crucial to handle these sources of uncertainty too, and even metrological organizations (ISO 1993) had to recognized it. For example, the ISO type B uncertainty is recommended to be ``evaluated by scientific judgment based on all the available information on the possible variability'' (ISO 1993) of the influence quantities (see also D'Agostini 1999c).