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

Area of Science:

• Statistical Auditing
• Bayesian Inference
• Quantitative Analysis

Background:

• Auditors assess financial statements by evaluating error quantiles against a materiality threshold.
• Dollar Unit Sampling (DUS) is a method where items are sampled proportionally to their book value.
• DUS generates a likelihood based on a high-dimensional parameter, while prior information pertains to a lower-dimensional subparameter (total error).

Purpose of the Study:

• To develop a Bayesian framework for statistical auditing using Dollar Unit Sampling (DUS).
• To address the challenge of processing partial prior information within the DUS methodology.
• To enable hypothesis testing and error estimation when prior information is limited to a subparameter.

Main Methods:

• Modification of the DUS likelihood function to align with available prior information.
• Adaptation of Bayes' theorem to the modified likelihood for Bayesian analysis.
• Utilization of a maximum entropy prior to incorporate limited auditor-specific information.

Main Results:

• A modified likelihood function is derived, compatible with partial prior information.
• A Bayesian approach is established to compute the posterior distribution for the total error subparameter.
• The study demonstrates that DUS can be a natural method for processing partial prior information in auditing.

Conclusions:

• The proposed methodology allows for Bayesian analysis in auditing even with incomplete prior information on a subparameter.
• The modified DUS approach provides a justified framework for auditors to incorporate limited prior knowledge.
• This research enhances the applicability of Bayesian methods in statistical auditing practices.