Complete experiment analysis and Bayesian inference in physics

Abstract

This thesis consists of three parts. The first part is concerned with complete experiment analysis. This is a theoretical topic within the field of Baryon spectroscopy and deals with the question of how many and which polarization observables have to be measured in order to un-ambiguously determine the underlying physical parameters of the hadronic reaction under consideration. The theorem of Moravcsik, which is based on graph theory and combinatorial methods, is applied to multiple reactions including two-pseudoscalar meson photoproduction, which is fully described by eight complex spin-amplitudes. This yields complete sets of observables, which are further reduced via numerical methods to contain only the minimal, required number of observables. The approach is appealing because the whole process can be automated, parallelized and is applicable to reactions with an arbitrary number of complex spin-amplitudes. The studies resulted in two papers published in the journal Physical Review C. <br/>

The second part of this thesis falls likewise into the domain of Baryon spectroscopy. The application of truncated partial-wave analysis on <em>η</em>-photoproduction data (<em>σ</em>₀, <em>Σ</em>, <em>T</em>, <em>E</em>, <em>F</em> and <em>G</em>) near the production threshold (<em>E</em>_<em>γ</em>^lab from 750 MeV to 1250 MeV) is studied. The results of the analysis are model-independent estimates of the electromagnetic multipole parameters and predictions for not yet measured polarization observables. For the first time, truncated partial-wave analysis and Bayesian inference are combined, resulting in parameter distributions instead of point estimates and accurate error estimates for the model parameters and predictions. The application of Bayesian inference is of interest, because it is a complementary analysis approach to the Frequentist method and the interpretation of the results differ. Furthermore, through the usage of Hamiltonian Monte Carlo, which is a special method of Markov chain Monte Carlo, the structure of arising solutions, i.e. the so-called ambiguities, can be studied. The results were published in Physical Review C. <br/>

The third part of this thesis falls into the domain of Neutrino mass analysis. It is connected to the second part of the thesis in the sense that the knowledge obtained about Bayesian inference is applied to a different analysis. Hence, Bayesian inference is used to analyze the first five measurement campaigns of the Karlsruhe Tritium Neutrino experiment, i.e. KNM1, KNM2, KNM3-SAP, KNM3-NAP, KNM4-NOM, KNM4-OPT and KNM5. The analysis are performed on Asimov data as well as for the measured data. Two approaches are taken, on the one hand each of the campaigns is analyzed on an individual basis. On the other hand, a so-called chained analysis of the campaigns is performed via multiple Bayesian knowledge updates. In this method, certain marginal parameter distributions of a former fit are used as prior information for the next fit. In addition, a sensitivity analysis is performed using different priors for the squared neutrino mass. However, in order to not delay the publication of this thesis, only the results on Asimov data are shown within this thesis. A paper containing the results on measurement data and further analyses is to be published in the near future.