Variations on KamLAND: likelihood analysis and frequentist confidence regions

In this letter the robustness of the first results from the KamLAND reactor neutrino experiment with respect to variations in the statistical analysis is considered. It is shown that an event-by-event based likelhood analysis provides a more powerful tool to extract information from the currently available data sample than a least-squares method based on energy binned data. Furthermore, a frequentist analysis of KamLAND data is performed. Confidence regions with correct coverage in the plane of the oscillation parameters are calculated by means of a Monte Carlo simulation. I find that the results of the usually adopted $\chi^2$-cut approximation are in reasonable agreement with the exact confidence regions, however, quantitative differences are detected. Finally, although the current data is consistent with an energy independent flux suppression, a $\sim 2\sigma$ indication in favour of oscillations can be stated, implying quantum mechanical interference over distances of the order of 200 km.