A Note on the Posterior Inference for the Yule-Simon Distribution

TL;DR

This paper introduces a Gibbs sampling method for Bayesian inference on the Yule-Simon distribution, demonstrating improved performance over frequentist methods in small sample scenarios through simulations and real data applications.

Contribution

It provides the first explicit Gibbs sampling scheme for the Yule-Simon distribution with a Gamma prior, enhancing Bayesian inference capabilities.

Findings

The Gibbs sampler performs well in simulations and real data.

Bayesian approach outperforms frequentist methods with small samples.

Application to text analysis demonstrates practical utility.

Abstract

The Yule--Simon distribution has been out of the radar of the Bayesian community, so far. In this note, we propose an explicit Gibbs sampling scheme when a Gamma prior is chosen for the shape parameter. The performance of the algorithm is illustrated with simulation studies, including count data regression, and a real data application to text analysis. We compare our proposal to the frequentist counterparts showing better performance of our algorithm when a small sample size is considered.