In the analysis of experimental data one may seek to solve a system of equations which is inconsistent. If the means and variances for the observed data are used, a least squares estimate of the solution of the system may be so improbable as to lead to the conclusion that some of the data should be discounted or ignored. Aposterioriprobability provides a rational means of attaching different weighting factors to the various data. If one assumes an aprioriprobability that the observed means and variances are correct and also some a priori probability that the distribution of errors has some alternative form, one can make use of Bayes technique to obtain a weighting of the data. A general description of this method is given and the method is then applied to a well-known problem of the determination of physical constants.