Bayesian Statistical Inference for Number Counting Experiments

Statistical inference describes how to infer about the true but unknown population from the measured sample and is a fundamental ingredient in scientific data analysis. Often one knows the probability model and wishes to estimate its parameters. The Bayesian approach provides a solution in terms of the posterior probability density function of the parameters of interest, given the model, the experimental result and our prior knowledge about the parameters. Number counting experiments are very often performed, in the assumption that the order in which results appear does not matter. Examples are the binomial model, arising when one investigates about the efficiency of a given selection process, and the Poisson model that describes how often a given outcome may show up. Here we provide analytic solutions for the Bayesian inference for both models, in case some or no prior information is available.