Markov Chain Monte Carlo for generating ranked textual data

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.