A Symbolic Computational Approach to a Problem Involving Multivariate Poisson Distributions

TL;DR

This paper introduces a symbolic computational method using WF Theory to compute conditional statistics of multivariate Poisson variables under linear constraints, with a new software tool and applications in biomolecular networks.

Contribution

It presents a novel symbolic approach and software implementation for analyzing constrained multivariate Poisson distributions, addressing problems in queuing and biomolecular networks.

Findings

Developed a symbolic computation package for constrained Poisson variables

Demonstrated applications in biomolecular network analysis

Provided algorithms for efficient conditional statistics calculation

Abstract

Multivariate Poisson random variables subject to linear integer constraints arise in several application areas, such as queuing and biomolecular networks. This note shows how to compute conditional statistics in this context, by employing WF Theory and associated algorithms. A symbolic computation package has been developed and is made freely available. A discussion of motivating biomolecular problems is also provided.