Confidence interval construction the difference in mean event rates for two Index independent , Poisson samples is discussed. Intervals are derived by considering Bayes estimates of the mean event rates using a family of noninformative priors. The coverage probabilities of the proposed are compared to those of the standard Wald interval for of observed events. A compromise method of constructing interval based on the data is suggested and its properties are evaluated. The method is illustrated in several examples.
Weissfeld, L. A., St. Laurent, R. T., Moulton, L. H., & St Laurent, R. T. (1991). Confidence intervals for the comparison of two Poisson distributions. Communications in Statistics, Theory and Methods, 20, 3071-3081. https://doi.org/10.1080/03610929108830688