The Bayesian Approach to Audit Evidence: Quantifying Statistical Evidence using the Bayes Factor

Abstract

The impact of statistical methods on the audit practice is growing because of the increasing availability of audit data and the statistical methods to analyze these data. A key aspect in the statistical approach to auditing is assessing the strength of evidence for or against a hypothesis. Unfortunately, the often-used frequentist statistical methods cannot provide the statistical evidence that audit standards demand directly nor easily. In this article we discuss an alternative approach that can provide this evidence: Bayesian inference. Firstly, we explore the philosophical differences between frequentist and Bayesian inference. Secondly, we discuss misconceptions in the interpretation of frequentist statistical evidence, and finally we discuss how Bayesian inference allows the auditor to obtain and interpret statistical evidence in line with audit standards via its alternative to the p value, the Bayes factor.

An Impartial Bayesian Hypothesis Test for Audit Sampling

“…However, from the posterior distribution alone the auditor is unable to quantify the evidence in the sample data for or against their claim. For this, the auditor needs to engage in an hypothesis test (Derks et al, 2021b).…”

“…Whereas NHST is commonly used, it cannot provide the auditor with direct evidence to support their statements (Wagenmakers, 2007), nor does it provide a good measure of the strength of the evidence that the sample provides for their statements (Berger & Sellke, 1987;Berkson, 1942;Dyckman, 2016;Edwards, Lindman, & Savage, 1963;Johnstone, 1994;Wagenmakers, 2007). We refer the reader to Johnstone (2021) and Derks et al (2021b) for a comprehensible explanation of this problem in the fields of accounting research and practice, respectively.…”

How to Incorporate Audit Information into the Statistical Model: Bayesian Generalized Linear Modeling for Audit Sampling

“…There are two reasons why this uniform prior distribution is often used in practice. First, it is easy to understand; second, with this prior, the Bayesian approach produces nearly identical results as a frequentist audit sampling procedure (Derks et al, 2022a). Therefore, we will use the Beta(1, 1) distribution as a prior for 𝜃𝜃 in the remainder of this section.…”

“…Auditors may want to compare several models and select the one that best describes the data. For this purpose, the Bayesian framework allows auditors to calculate the Bayes factor, a measure that quantifies the statistical evidence in favor of one model over another model (Kass & Raftery, 1995;Fragoso, 2018;Derks et al, 2022a). By quantifying and comparing the evidence for multiple models (e.g., a model with and a model without a specific covariate), auditors can assess whether the addition of a parameter to the model has a meaningful impact on the model predictions.…”

“…For example, Bayesian statistics allows for the inclusion of pre-existing information about the misstatement in the sample evaluation (Derks et al, 2021a), and it facilitates the continuous monitoring of evidence over time (Rouder, 2014;Wagenmakers, Lee, Lodewyckx, & Iverson, 2008). Furthermore, the Bayesian approach is advocated as a good fit for auditing practice because it is relatively simple to understand for auditors and stakeholders of the audit (Stewart, 2013;Derks et al, 2022a). This article is structured as follows.…”