  Frequentist (classical) and the Bayesian approaches to the construction of
confidence limits are compared. Various examples which illustrate specific
problems are presented. The Likelihood Principle and the Stopping Rule Paradox
are discussed. The performance of the different methods is investigated
relative to the properties coherence, precision, bias, universality,
simplicity. A proposal on how to define error limits in various cases are
derived from the comparison. They are based on the likelihood function only and
follow in most cases the general practice in high energy physics. Classical
methods are not recommended because they violate the Likelihood Principle, they
can produce physically inconsistent results, suffer from lack of precision and
generality. Also the extreme Bayesian approach with arbitrary choice of the
prior probability density or priors deduced from scaling laws is rejected.
