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Fonseca, PMT da (2016)

Digit analysis using Benford's Law: A Bayesian approach

Masters Thesis, ISEG - Instituto Superior de Economia e Gestão, Lisbon School of Economics & Management, Portugal.

ISSN/ISBN: Not available at this time. DOI: Not available at this time.

Abstract: According to Benford's law, many of the collections of numbers which are generated without human intervention exhibit a logarithmically decaying pattern in leading digit frequencies. Through digit analysis, this empirical regularity can help identifying erroneous or fraudulent data. Due to the power that classical significance tests with fixed dimension attain in large samples, they produce small p-values and, if the sample is big enough, are able to identify any deviation from Benford's law, no matter how tiny, as statistically significant. This may result in the rejection of Benford's law in samples where the deviations from it are without practical importance, and consequently samples which are legit are likely to be classified as erroneous or fraudulent. This dissertation proposes a Bayesian model selection approach to digit analysis. An empirical application with macroeconomic statistics from Eurozone countries demonstrates the applicability of the suggested methodology and explores the conflict between the p-value and Bayesian measures of evidence (Bayes factors and posterior probabilities) in the support they provide to the presence of Benford's law in a given sample. It is concluded that classical significance tests often reject the presence of Benford's law in samples which are deemed to be in conformance to it by Bayesian measures, and that even lower bounds on such measures over wide classes of prior distributions often provide more evidence in favour of Benford's law than the p-value and classical significance tests seem to suggest.

@mastersthesis{, author={Fonseca, Pedro Miguel Teles da}, title = {Digit analysis using Benford's Law: A Bayesian approach}, year={2016}, institution={ISEG - Instituto Superior de Economia e Gest{'~a}o, Lisbon School of Economics \& Management}, url={{}}, }

Reference Type: Thesis

Subject Area(s): Economics, Statistics