On a representation of partially-distinguishable populations

TL;DR

This paper introduces a new way to represent heterogeneous stochastic populations with varying distinguishability levels, linking independent instances to point processes on probability measures, ensuring a constructive and meaningful approach.

Contribution

It presents a novel, fully constructive representation for heterogeneous populations with different distinguishability levels, connecting to point processes on probability measures.

Findings

Representation relates to point processes on probability measures

Ensures meaningfulness through a constructive approach

Applicable to populations with varying distinguishability levels

Abstract

A representation of heterogeneous stochastic populations that are composed of sub-populations with different levels of distinguishability is introduced together with an analysis of its properties. It is demonstrated that any instance of this representation where individuals are independent can be related to a point process on the set of probability measures on the individual state space. The introduction of the proposed representation is fully constructive which ensures the meaningfulness of the approach.