A nested sampling approach to Bayesian analysis for KamLAND-Zen 800

We present a Python-based Bayesian analysis using nested sampling to investigate the KamLAND-Zen 800 data for neutrinoless double beta (0νββ) decay in Xe-136. This analysis uses a Bayesian framework to efficiently explore the combined signal + background prior space and calculate the Bayesian evidences for various values for the neutrinoless double beta decay rate. From the KamLAND-Zen 800 dataset, which includes 2097 kg·yr of Xe-136 exposure in an ultra-low-radioactivity environment, we find no significant evidence of 0νββ decay. For the entire KLZ-800 only dataset, without including the previous KLZ-400 exposure, evidence for a 0νββ signal has been rejected leading to a lower half-life limit of 3.4 x 10^26 years at 90 percent credibility level. This work provides a complementary analysis to the Frequentist and Bayesian MCMC approaches and provides a statistical framework for future investigations.