Simulations of nuclear reactor physics can disagree significantly from experimental evidence, even when the most accurate models are used. An important part of this bias from experiment is caused by nuclear data. The nuclear data have inherent uncertainties due to the way they are evaluated, which then propagate to nuclear reactor simulations. This creates a bias and an uncertainty in a predicted reactor parameter like \keff~or the composition of spent fuel. This thesis focuses on data assimilation techniques to ameliorate the effects of nuclear data. Data assimilation takes integral experiments and assimilates them in a Bayesian way to improve simulations. It can also be used to find trends and areas needing improvement in evaluated nuclear data. The research focuses on advancing the data assimilation theory and knowledge used in reactor physics, especially on techniques that require stochastic sampling of the nuclear data. Furthermore, the research takes advantage of rich experimental data available from the Proteus research reactor at the Paul Scherrer Institute. The thesis showed, for the first time, that two methods based on stochastic sampling (called MOCABA and BMC) gave equivalent results to each other and to the traditional method called GLLS. This was corroborated with two independent studies that used different experiments, neutron transport codes, nuclear data, and processing codes. The first study used the JEZEBEL-Pu239 benchmark, the Serpent2 neutron transport code, and NUSS. The second study used reactivity experiments from the LWR-Phase II experiments at Proteus, CASMO-5 for neutron transport, and SHARK-X. While using Serpent2, several questions pertaining to the stochastic uncertainty of its sensitivity coefficients arose. To address these, a new method called eXtended GLLS, or xGLLS, was proposed and tested in the thesis. xGLLS showed that the uncertainties associated with sensitivity coefficients have a negligible effect on the data assimilation as long as the calculated integral parameters themselves were converged. The final study focused on adjusting the fission yields and covariances made by the GEF code with post-irradiation examination experiments from Proteus. The adjustment improved the accuracy of predicted nuclide concentrations in spent fuel and improved the agreement between the GEF fission yields and those of ENDF/B-VIII.0 and JEFF3.3.