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Open AccessArticle

Bayesian Inference in Auditing with Partial Prior Information Using Maximum Entropy Priors

1
Department of Quantitative Methods, University of Las Palmas de Gran Canaria, 35001 Las Palmas de Gran Canaria, Spain
2
Department of Quantitative Methods, University of Granada, 18071 Granada, Spain
*
Author to whom correspondence should be addressed.
All three authors contributed equally to this work.
Entropy 2018, 20(12), 919; https://doi.org/10.3390/e20120919
Received: 15 October 2018 / Revised: 15 November 2018 / Accepted: 28 November 2018 / Published: 1 December 2018
(This article belongs to the Special Issue Bayesian Inference and Information Theory)
Problems in statistical auditing are usually one–sided. In fact, the main interest for auditors is to determine the quantiles of the total amount of error, and then to compare these quantiles with a given materiality fixed by the auditor, so that the accounting statement can be accepted or rejected. Dollar unit sampling (DUS) is a useful procedure to collect sample information, whereby items are chosen with a probability proportional to book amounts and in which the relevant error amount distribution is the distribution of the taints weighted by the book value. The likelihood induced by DUS refers to a 201–variate parameter p but the prior information is in a subparameter θ linear function of p , representing the total amount of error. This means that partial prior information must be processed. In this paper, two main proposals are made: (1) to modify the likelihood, to make it compatible with prior information and thus obtain a Bayesian analysis for hypotheses to be tested; (2) to use a maximum entropy prior to incorporate limited auditor information. To achieve these goals, we obtain a modified likelihood function inspired by the induced likelihood described by Zehna (1966) and then adapt the Bayes’ theorem to this likelihood in order to derive a posterior distribution for θ . This approach shows that the DUS methodology can be justified as a natural method of processing partial prior information in auditing and that a Bayesian analysis can be performed even when prior information is only available for a subparameter of the model. Finally, some numerical examples are presented. View Full-Text
Keywords: auditing; Bayesian inference; dollar unit sampling; modified likelihood; partial prior information auditing; Bayesian inference; dollar unit sampling; modified likelihood; partial prior information
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Martel-Escobar, M.; Vázquez-Polo, F.-J.; Hernández-Bastida, A. Bayesian Inference in Auditing with Partial Prior Information Using Maximum Entropy Priors. Entropy 2018, 20, 919.

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