Binned Likelihood including Monte Carlo Statistical Uncertainty in Bayesian Inference

Abstract

Data analysis in HEP experiments often uses binned likelihood from data and finite Monte Carlo sample. Statistical uncertainty of Monte Carlo sample has been introduced in Frequentist Inference in some literatures, but they are not suitable for Bayesian Inference. This technical note introduces the binned likelihood with Monte Carlo statistical uncertainty in Bayesian Inference and includes the derivation of it. It turns out that the results are similar to the results in [1]. But this tech-note gives an alternate and more intuitive derivation of the content