Development of a tool for Bayesian data analysis and its application in Monte Carlo tuning

Abstract

In this thesis, a novel approach to Monte Carlo event generator tuning, grounded in Bayesian reasoning, is presented. The Bayesian Analysis Toolkit (BAT.jl) is introduced as a modern tool for performing Bayesian inference. A numerical test suite that verifies the validity and performance of the BAT.jl package is developed. The test suite is used to evaluate the performance of the Markov chain Monte Carlo (MCMC) sampling algorithms implemented in BAT.jl, utilizing a selection of test functions and different metrics to quantify the quality of the samples. The results show that the MCMC algorithms are able to sample the posterior distributions of the test functions accurately. Utilizing the BAT.jl toolkit, two hadronization models within the Herwig Monte Carlo event generator (MCEG) are successfully tuned to data from the LEP experiments. Several aspects of the tuning procedure are investigated, such as parameter and observable selection and parametrization quality. Samples generated using the tuned parameters, obtained from the global mode of the posterior, are compared to data through a χ2 test. The resulting p-values for the tuned simulations significantly outperform those from the nominal MCEG samples, indicating a successful tune and an improved description of the data. The posterior is also used to present a method for propagating the parameter uncertainties to the realm of the observables, providing a measure for the tuning uncertainty. Studies on the impact of assigning weights to the observables and the impact of correlations between measurements on the tuning are also presented. These show that weights can alter the tuning results, especially in cases with multiple modes in the posterior. However, their influence on the quality of the tune is minimal in this case. The correlation of measurements has less of an impact on the position of the global mode but substantially affects the associated parameter uncertainties estimates. Finally, a comparison of the two tuned hadronization models is presented, which indicates that the Lund string model describes the data slightly better than the cluster hadronization model for this set of observables.