# Application of Bayes' theorem for pulse shape discrimination

## TL;DR

This paper introduces a Bayesian method for pulse shape discrimination that assigns confidence probabilities to classify photons and neutrons individually, adapting to varying ratios and outperforming traditional decision boundary methods.

## Contribution

The study presents a novel Bayesian approach with an iterative scheme for adaptive probability space, improving neutron detection and ratio estimation in pulse shape discrimination.

## Key findings

- Achieved up to 90% neutron acceptance at photon-to-neutron ratios of 2000
- Performed 9% better than decision boundary approach
- Effectively adapted probability space with increasing photon counts

## Abstract

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.