Estimating the distribution of marks of a homogeneous marked Poisson process

TL;DR

This paper introduces a maximum likelihood estimator for the distribution of event types in a homogeneous Poisson process, with proven consistency, asymptotic normality, and applications to neutron detection.

Contribution

It provides explicit solutions for the estimator, including order restricted variants, and addresses the associated Sylvester-Ramanujan system of equations.

Findings

Estimator is strongly consistent and asymptotically normal.

Explicit maximum likelihood estimator derived for event distribution.

Application demonstrated in neutron detection at European Spallation Source.

Abstract

In this paper we propose an estimator of the distribution of events of different kinds in a homogeneous Poisson process. We give an explicit solution for the maximum likelihood estimator of the distribution and derive its strong consistency and asymptotic normality. We also provide an order restricted estimator of the distribution and derive its consistency and asymptotic distribution. The inference problem gives rise to a Sylvester-Ramanujan system of equations. We discuss application of the estimator to the detection of neutrons in a novel detector developed at the European Spallation Source in Lund, Sweden.