On the relation between frequentist and Bayesian approaches for the case   of Poisson statistics
  We propose modified frequentist definition for the determination of confidence intervals for the case of Poisson statistics. Namely, we require that 1-\beta' \geq \sum_{n=o}^{n_{obs}+k} P(n|\lambda) \geq \alpha'. We show that this definition is equivalent to the Bayesian method with prior \pi(\lambda) \sim \lambda^{k}. We also propose modified frequentist definition for the case of nonzero background. 
Sergey Bitioukov and Nikolai Krasnikov
physics.data-an stat.ME