  The Taishan Antineutrino Observatory (TAO) is a liquid-scintillator satellite
experiment of the Jiangmen Underground Neutrino Observatory (JUNO) to measure
the reference reactor neutrino spectrum with sub-percent energy resolution. We
use inhomogeous Poisson process and Tweedie generalized linear model (GLM) to
calibrate the detector response and the charge distribution of a SiPM. We
develop a pure probabilistic method using time and charge of SiPMs from first
principles to reconstruct point-like events in the TAO central detector. Thanks
to our precise model and the high photo-coverage and quantum efficiency of the
SiPM tiles at TAO, we achieve a vertex position resolution better than 16 mm
and an energy resolution of about 2% at 1 MeV, marking the world's best
performance of liquid scintillator detectors. Our methodology is applicable to
other experiments that utilize PMTs for time and charge readouts.
