  The extraction of any physical information from quasielastic neutron
scattering spectra is generally done by fitting a model to the data by means of
chi-square minimization procedure. However, as pointed out by the pioneering
work of D.S. Sivia et al., also another probabilistic approach based on Bayes
theorem can be employed. In a nutshell, the main difference between the
classical chi-square minimization and the Bayesian approach is the way of
expressing the final results: In the first case, the result is a set of values
of parameters with a symmetric error and a figure of merit such as chi-square,
whereas in the second case the results are presented as probability
distribution functions (PDF) of both, parameters and merit figure. In this
contribution, we demonstrate how final PDFs are obtained by exploring all
possible combinations of parameters that are compatible with the experimental
error. Three advantages of this method will be emphasized: First, correlations
between parameters are automatically taken into account, which implies, for
example, that parameter errors are correctly calculated, correlations show up
in a natural way and ill defined parameters are immediately recognized from
their PDF. Second, it is possible to calculate the likelihood of a determined
physical model, and therefore to select the one among many that fits the data
best with a minimal number of parameters, in a correctly defined probabilistic
way.
