Universal deterministic patterns in stochastic count data

TL;DR

This paper uncovers universal deterministic patterns in the mean-Fano factor relationship across diverse stochastic count datasets, supported by a theoretical model linking these patterns to sample size.

Contribution

It introduces a theory explaining the emergence of these patterns from discrete distributions organized in matrix form, highlighting their dependence on sample size.

Findings

Patterns are observed across genomics, citations, ecology, and more.

Theoretical model accurately predicts the patterns.

Patterns depend solely on sample size.

Abstract

We report the existence of deterministic patterns in plots showing the relationship between the mean and the Fano factor (ratio of variance and mean) of stochastic count data. These patterns are found in a wide variety of datasets, including those from genomics, paper citations, commerce, ecology, disease outbreaks, and employment statistics. We develop a theory showing that the patterns naturally emerge when data sampled from discrete probability distributions is organised in matrix form. The theory precisely predicts the patterns and shows that they are a function of only one variable - the sample size.