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##

Reweighting of conditional inferences

The values of the influence variables and their uncertainties
contribute to our background knowledge about the experimental
measurements. Using to represent our very general background
knowledge, the posterior pdf
will then be
, where the dependence on
all possible values of
has been made explicit. The
inference that takes into account the uncertain vector
is
obtained using the rules of probability (see Tab. 1)
by integrating the joint probability over the uninteresting
influence variables:

As a simple, but important case, let us consider a single
influence variable given by an additive instrumental offset
, which is expected to
be zero because the instrument has been calibrated as well as feasible and
the remaining uncertainty is . Modelling our
uncertainty in as a Gaussian distribution with a standard
deviation , the posterior for is

The result is that the net variance is the sum of
the variance in the measurement and the variance in the influence variable.

** Next:** Joint inference and marginalization
** Up:** Uncertainties from systematic effects
** Previous:** Uncertainties from systematic effects
Giulio D'Agostini
2003-05-13