``Statistical'' uncertainties arise from variations in the results of repeated observations under (apparently) identical conditions. They vanish if the number of observations becomes very large (``the uncertainty is dominated by systematics'' is the typical expression used in this case) and can be treated -- in most cases, but with some exceptions of great relevance in High Energy Physics -- using conventional statistics based on the frequency-based definition of probability.

On the other hand, it is not possible to treat
``systematic'' uncertainties coherently in the
frequentistic framework. Several ad hoc prescriptions for how
to combine ``statistical'' and ``systematic'' uncertainties
can be found in textbooks and in the literature:
*``add them linearly''*;
*``add them linearly if , else add them
quadratically''*;
*``don't add them at all''*, and so on (see, e.g.,
Part 3 of Ref. [1]). The ``fashion'' at the moment is to
add them quadratically if they are considered
independent, or to build a covariance matrix of ``statistical''
and ``systematic'' uncertainties
to treat general cases.
These procedures are not justified by conventional
statistical theory, but they are accepted
because of the pragmatic good sense of physicists.
For example, an experimentalist may be
reluctant to add twenty or more
contributions linearly to evaluate the uncertainty
of a complicated measurement, or decides
to treat
the correlated ``systematic'' uncertainties
``statistically'', in both cases
unaware of, or simply not caring about, violating
frequentistic principles.

The only way to deal with these and related
problems in a consistent way
is to abandon the frequentistic interpretation
of probability introduced at the beginning of this century,
and to recover the intuitive concept of probability
as *degree of belief*. Stated differently, one needs to associate
the idea of probability with the lack of knowledge,
rather than to the outcome of repeated experiments.
This has been recognized also by the International Standardization Organization(ISO) which assumes the
subjective definition of probability
in its
*``Guide to the expression of uncertainty in measurement''*[3].

This primer is organized as follows:

- Sections - give a general introduction to subjective probability.
- Sections - summarize some concepts and formulae concerning random variables, needed for many applications.
- Section introduces the problem of measurement uncertainty and deals with the terminology.
- Sections - present the inferential model.
- Sections - show several physical applications of the model.
- Section deals with the approximate methods needed when the general solution becomes complicated; in this context the ISO recommendations will be presented and discussed,
- Section deals with uncertainty propagation. It is particularly short because, in this scheme, there is no difference between the treatment of ``systematic'' uncertainties and indirect measurements; the section simply refers to the results of Sections -.
- Section is dedicated to a detailed discussion about the covariance matrix of correlated data and the trouble it may cause.
- Section was added as an example of a more complicated inference (multidimensional unfolding) than those treated in Sections -.