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The extraction of any physical information from quasielastic neutronscattering spectra is generally done by fitting a model to the data by means ofchi-square minimization procedure. However, as pointed out by the pioneeringwork of D.S. Sivia et al., also another probabilistic approach based on Bayestheorem can be employed. In a nutshell, the main difference between theclassical chi-square minimization and the Bayesian approach is the way ofexpressing the final results: In the first case, the result is a set of valuesof parameters with a symmetric error and a figure of merit such as chi-square,whereas in the second case the results are presented as probabilitydistribution functions (PDF) of both, parameters and merit figure. In thiscontribution, we demonstrate how final PDFs are obtained by exploring allpossible combinations of parameters that are compatible with the experimentalerror. Three advantages of this method will be emphasized: First, correlationsbetween parameters are automatically taken into account, which implies, forexample, that parameter errors are correctly calculated, correlations show upin a natural way and ill defined parameters are immediately recognized fromtheir PDF. Second, it is possible to calculate the likelihood of a determinedphysical model, and therefore to select the one among many that fits the databest with a minimal number of parameters, in a correctly defined probabilisticway.

Bayesian Analysis of QENS data: From parameter determination to model selection