The Applicability of Bayesian Statistics in Auditing

Abstract

The basic purpose of this study was the investigation of the usefulness of Bayesian statistical techniques to problems of estimation in the field of auditing. By using subjective probabilities the auditor can explicitly bring prior knowledge to bear on his problem by incorporating his feelings in the sampling process and thus obtain an efficient method by which refined estimates can be obtained. The results of the study strongly support the premise that the auditor can obtain superior results from the Bayesian model in estimating unknown quantities as opposed to those obtained through either the non-statistical approach or the classical statistical approach.In a recent monograph, the statement was made that "the objectives of Accounting are to provide information for the following purposes: [ 4 ] , which were then outlined. The nub of the monograph is contained in the phrase "to provide (relevant ) information." Just what is information? Shannon's concept of information was the resolvement of Uncertainty.' Using the concept of information as the displacement of uncertainty, we would expect that the standards used in certifying financial statements would have been so rigorously and meticulously defined that there would be no room left for uncertainty. However, upon investigation, we find that this is not the case. For example, "The public is nonplussed where under the same circumstances two or more widely different sets of figures are 'certified by us. To pursue that unmerry way is to make the ground beneath us shaky." 'The above statement is not too surprising, since accountants often work with incomplete data. However, what is surprising is that accountants have not made more use of statistical samples, statistical influence, and other statistical concepts and techniques in reducing areas of uncertainty.Accountants in general and auditors specifically must make decisions or render judgments from limited or partial information.

An Impartial Bayesian Hypothesis Test for Audit Sampling

“…Applying this prior distribution confers two advantages to the auditor. Firstly, incorporating existing information into the prior distribution means there is more available information at the start of substantive testing, which generally allows for a more efficient estimate of the population misstatement (Knoblett, 1970). Secondly, since the prior distribution partly determines the predictions from the auditor's hypothesis, the information in the prior distribution is incorporated directly into a hypothesis test.…”

Priors in a Bayesian audit: How integration of existing information into the prior distribution can improve audit transparency and efficiency

“…Second, the translation from relevant audit information into a prior probability distribution is perceived as difficult (Abdolmohammadi 1985;Abdolmohammadi 1987;Corless 1972). Nevertheless, by overcoming these hurdles the auditor can build upon existing information in a coherent manner, resulting in concrete advantages -such as a more accurate estimation of the population misstatement (Knoblett 1970) and audit risk (Stewart 2013), a potential reduction in sample size, and formalized predictions-that can increase efficiency and transparency in audit sampling. Furthermore, it has been shown in earlier studies based on the well-known audit populations from Neter and Loebbecke (1975) that Bayesian methods result in upper bounds that achieve nominal coverage (Chan and Smieliauskas 1990;Swinamer, Lesperance, and Will 2007).…”

Priors in a Bayesian Audit: How Integration of Existing Information into the Prior Distribution Can Improve Audit Transparency and Efficiency

“…Second, the translation from relevant audit information into a prior probability distribution is perceived as difficult (Abdolmohammadi 1985;Abdolmohammadi 1987;Corless 1972). Nevertheless, by overcoming these hurdles the auditor can build upon existing information in a coherent manner, resulting in concrete advantages -such as a more accurate estimation of the population misstatement (Knoblett 1970) and audit risk (Stewart 2013), a potential reduction in sample size, and formalized predictions-that can increase efficiency and transparency in audit sampling. To make these tangible advantages of Bayesian statistics more easily available for auditors, we will introduce five methods for incorporating existing audit information into a prior probability distribution.…”