  A Bayesian approach is proposed for pulse shape discrimination of photons and
neutrons in liquid organic scinitillators. Instead of drawing a decision
boundary, each pulse is assigned a photon or neutron confidence probability.
This allows for photon and neutron classification on an event-by-event basis.
The sum of those confidence probabilities is used to estimate the number of
photon and neutron instances in the data. An iterative scheme, similar to an
expectation-maximization algorithm for Gaussian mixtures, is used to infer the
ratio of photons-to-neutrons in each measurement. Therefore, the probability
space adapts to data with varying photon-to-neutron ratios. A time-correlated
measurement of Am-Be and separate measurements of $^{137}$Cs, $^{60}$Co and
$^{232}$Th photon sources were used to construct libraries of neutrons and
photons. These libraries were then used to produce synthetic data sets with
varying ratios of photons-to-neutrons. Probability weighted method that we
implemented was found to maintain neutron acceptance rate of up to 90% up to
photon-to-neutron ratio of 2000, and performed 9% better than decision boundary
approach. Furthermore, the iterative approach appropriately changed the
probability space with an increasing number of photons which kept the neutron
population estimate from unrealistically increasing.
