Speaker
Description
Bayesian analysis provides an essential transition from traditional frequentist methods, where probability defines the long-term frequency of events, to a framework that expresses probability as a degree of belief about the occurrence of an event or the validity of a hypothesis. This conceptual divergence is crucial in Parity Violating Electron Scattering (PVES) experiments, such as QWeak and MOLLER, where high precision is critically important.
Bayesian statistics utilize Bayes' theorem to integrate prior information and new observed data into a comprehensive posterior distribution. This approach enables direct probabilistic inferences and decision-making under uncertainty, enhancing the accuracy of experimental corrections significantly. It accounts for correlations between parameters, such as asymmetry components, by forming the posterior based on measured data, thereby providing a more accurate and realistic estimation of these parameters. Advanced computational techniques, including Hamiltonian Monte Carlo (HMC) and the No U-Turn Sampler (NUTS), are employed to efficiently navigate the complex, high-dimensional posterior distributions.
Our results demonstrate that Bayesian-fitted values align more closely with precise measurements in the Qweak experiment and simulation outcomes in the MOLLER experiment than traditional frequentist approaches. This enhanced precision is crucial for enhancing our comprehension of particle, nuclear, and hadronic physics and mitigating the impact of uncontrollable factors, including deviations in beam direction and discrepancies in spin alignment. The efficacy of Bayesian analysis in enhancing the precision of crucial experiments underscores its transformative potential in the field.
We acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC).
