Experimental signs pointing to a Bayesian instead of a classical approach for experiments with a small number of events

The Bayesian and anti-Bayesian approaches to compute confidence intervals for the Poisson and binomial distributions are recalled. A choice has to be made between both approaches to be able to predict the best confidence intervals for an expected cross section or a branching ratio in the case of experiments with a small number of events. To decide which approach is the most correct in these cases, we perform a large number of identically repeated measurements of two quantities: the occurrence of small numbers, and the ratio of small numbers, and we note the number of success for each approach, where success means that the predicted confidence interval encloses the true value of each quantity. It is shown that the approach giving the ratio success/trials closest to the 68.3% probability content expected — by construction of the confidence belts — is the Bayesian scheme with an priori uniform distribution.