When we have many uncertain influence factors and/or the model of uncertainty is non-Gaussian, the analytic solution of Eq. (73), or Eqs. (77)-(79) can be complicated, or not existing at all. Then numeric or approximate methods are needed. The most powerful numerical methods are based on Monte Carlo (MC) techniques (see Sect. 9 for a short account). This issue goes beyond the aim of this report. In a recent comprehensive particle-physics paper by Ciuchini et al (2001), these ideas have been used to infer the fundamental parameters of the Standard Model of particle physics, using all available experimental information.
For routine use, a practical approximate method can be developed by
thinking of the value inferred for the expected value of
as a raw value, indicated with , that is,
(`raw' in the sense that it needs later to be `corrected'
for all possible value of
, as it will be clear in a while).
The value of , which depends on the possible values of
, can be seen as a function of and