Markov Chain Monte Carlo for generating ranked textual data

TL;DR

This paper introduces a Markov Chain Monte Carlo approach, specifically the Metropolis-Hastings algorithm, to analyze the rank-size distribution of words in text, demonstrating its effectiveness on US Presidential speeches and supporting its broader applicability.

Contribution

It presents a novel application of MCMC methods to rank-size law analysis in text data, establishing a Markov chain model for hapax legomena and validating its consistency through extensive statistical tests.

Findings

Hapax legomena follow a Markov chain of order one.

The method confirms the stochastic structure of rank-size distributions.

Hapaxes are characterized as rare, memory-less events.

Abstract

This paper faces a central theme in applied statistics and information science, which is the assessment of the stochastic structure of rank-size laws in text analysis. We consider the words in a corpus by ranking them on the basis of their frequencies in descending order. The starting point is that the ranked data generated in linguistic contexts can be viewed as the realisations of a discrete states Markov chain, whose stationary distribution behaves according to a discretisation of the best fitted rank-size law. The employed methodological toolkit is Markov Chain Monte Carlo, specifically referring to the Metropolis-Hastings algorithm. The theoretical framework is applied to the rank-size analysis of the hapax legomena occurring in the speeches of the US Presidents. We offer a large number of statistical tests leading to the consistency of our methodological proposal. To pursue our scopes, we also offer arguments supporting that hapaxes are rare (``extreme") events resulting from memory-less-like processes. Moreover, we show that the considered sample has the stochastic structure of a Markov chain of order one. Importantly, we discuss the versatility of the method, which is considered suitable for deducing similar outcomes for other applied science contexts.