  Photomultiplier tubes (PMT) are widely deployed at neutrino and dark matter
experiments for photon counting. When multiple photons hit a PMT consecutively,
their photo-electron (PE) pulses pile up to hinder the precise measurements of
the count and timings. We introduce Fast Stochastic Matching Pursuit (FSMP) to
analyze the PMT signal waveforms into individual PEs with the strategy of
reversible-jump Markov-chain Monte Carlo. We demonstrate that FSMP improves the
energy and time resolution of PMT-based experiments, gains acceleration on GPUs
and is extensible to microchannel-plate (MCP) PMTs with jumbo-charge outputs.
In the condition of our laboratory characterization of 8-inch MCP-PMTs, FSMP
improves the energy resolution by up to 12% from the long-serving method of
waveform integration.
