Bayesian Analysis of Many-Pole Fits of Hadron Propagators in Lattice QCD

A common procedure in Lattice QCD is to calculate a correlation function in a certain channel and then fit it as a sum of several exponentials [1– 4]. The parameters of the fits are estimated by minimizing χ. To find the errors, ideally the calculations should be repeated many times, but this is impractical. Usually the jacknife or the bootstrap is performed. Instead here we use Bayes’s theorem to derive the parameters’ probability distribution for given data from the probability of the data for given parameters. Usually one determines the number of poles by comparing χ for different models. It is very often ambiguous. Here we use the parameters probability distribution to calculate relative probabilities of the possible models with given data. We perform the Bayesian analysis for some model functions imitating Lattice QCD propagators. Then we apply this method to analyze SU(2) hadron propagators.