From chi-squared to Bayesian model comparison and Levy expansions of Bose-Einstein correlations in e+e- reactions

The usual chi-squared method of fit quality assessment is a special case of the more general method of Bayesian model comparison which involves integrals of the likelihood and prior over all possible values of all parameters. We introduce new parametrisations based on systematic expansions around the stretched exponential or Fourier-transformed L\'evy source distribution, and utilise the increased discriminating power of the Bayesian approach to evaluate the relative probability of these models to be true representations of a recently measured Bose-Einstein correlation data in e+e- annihilations at LEP.