Evaluating statistical uncertainties and correlations using the bootstrap method

The bootstrap method is a powerful technique to evaluate the statistical uncertainty of a measurement and correlations between bins. This method uses a set of replicas of the nominal dataset, derived by introducing Poisson perturbations corresponding to statistical fluctuations. Each replica is then analyzed in the same way as the nominal dataset to arrive at a set of replica measurements. The statistical uncertainty and correlations can then be extracted from these replica measurements. This note describes a version of the bootstrap method suitable for data analysis in high energy physics and provides an associated software implementation. Various applications are discussed, such as determining the statistical error on systematic uncertainties. A novel feature of the provided software is that the fluctuations that generate the bootstrap replicas are deterministic. This makes it is possible to evaluate statistical correlations between measurements that are using fully or partially overlapping input data, even if the associated analyses are performed by different teams, or years apart.