Integrating Statistical and Non-Statistical Evidence Using Belief Functions (original) (raw)
Related papers
International Journal of Intelligent Systems, 1994
The main purpose of this article is to show how one can integrate statistical and nonstatistical items of evidence under the belief function framework. First, we use the properties of consonant belief functions to define the belief that the true mean of a variable lies in a given interval when a statistical test is performed for the variable. Second, we use the above definition to determine the sample size for a statistical test when a desired level of belief is needed from the sample. Third, we determine the level of belief that the true mean lies in a given interval when a statistical test is performed for the variable with a given sample size. We use an auditing example to illustrate the process.
Attribute Sampling: A Belief-Function Approach to Statistical Audit Evidence
AUDITING: A Journal of Practice & Theory, 2000
The Dempster-Shafer belief function framework has been used to model the aggregation of audit evidence based on subjectively assessed beliefs. This paper shows how statistical evidence obtained by means of attribute sampling may be represented as belief functions, so that it can be incorporated into such models. In particular, the article shows: (1) how to determine the sample size in attribute sampling to obtain a desired level of belief that the true attribute occurrence rate of the population lies in a given interval; (2) what level of belief is obtained for a specified interval, given the sample result. As intuitively expected, we find that the sample size increases as the desired level of belief in the interval increases. In evaluating the sample results, our findings are again intuitively appealing. For example, provided the sample occurrence rate falls in the interval B for a given number of occurrences of the attribute, we find that the belief in B, Bel(B), increases as the ...
A Bayesian perspective on the strength of evidence in auditing
1992
This paper deals with a mathematical definition of the strength of evidence in the Bayesian framework for the (1) positive evidence, (2) negative evidence, and (3) confirming evidence. These concepts are important in auditing. The earlier definitions of these concepts by Toba and Kissinger depend on the prior probability and the posterior probability and thus lead to inconsistencies. The definitions discussed in this paper are based on the likelihood ratio and thus depend on the intrinsic properties of the evidence and therefore are free from the inconsistencies encountered in the Toba-Kissinger framework.
The belief-function approach to aggregating audit evidence
International Journal of Intelligent Systems, 1995
In this article, we present the belief-function approach to aggregating audit evidence. The approach uses an evidential network to represent the structure of audit evidence. In turn, it allows us to treat all types of dependencies and relationships among accounts and items of evidence, and thus the approach should help the auditor conduct an efficient and effective audit.
Structural analysis of audit evidence using belief functions
Fuzzy Sets and Systems, 2002
This article performs two types of analysis using Dempster-Shafer theory of belief functions for evidential reasoning. The ÿrst analysis deals with the impact of the structure of audit evidence on the overall belief at each variable in the network, variables being the account balance to be audited, the related transaction streams, and the associated audit objectives. The second analysis deals with the impact of the relationship (logical 'and' and 'algebraic relationship') among various variables in the network on the overall belief. For our ÿrst analysis, we change the evidential structure from a network to a tree and determine its impact.
2014
In auditing the problem of testing hypotheses about frequency of incorrect items is considered. It is treated as the particular case of compliance testing problems. Usually, classical statistical tests are used to testing those types of hypotheses. In the paper the Bayesian approach will be considered. The hypothesis will be tested on the basis of the simple random sample or on the basis of the simple random sample drawn from strata. Usually, Bayesian statistical inference in auditing is based on confidence intervals. Here, instead of that two well known Bayesian rules will be considered. Presented procedures will be illustrated by means of empirical examples.
Auditors’ Evaluations of Uncertain Audit Evidence: Belief Functions versus Probabilities
Studies in Fuzziness and Soft Computing, 2002
, and Van den Acker have identified appealing features of belief function evidential networks. These networks can express the support that audit evidence provides for assertions, accounts and financial statements. These networks can also aggregate many pieces of evidence into an overall level of support for a particular assertion, account or an entire set of financial statements.
THEORETICAL INVESTIGATION OF BELIEF REVISIONS IN AUDITING
ku.edu
In this paper we examine the empirical findings of belief revision under two alternatives: the Bayesian framework and the Dempster-Shafer theory of belief functions. Bayesian theory is very stringent in its requirement that the probability of mu tually exclusive and collectively exhaustive events sum to one. It requires that the belief be increased in light of supporting evidence, and be decreased in light of conflicting evidence. These results are consistent with the empirical findings. However, the Bayesian analysis entails the largest increase (decrease) in belief for medium priors in light of supporting (conflicting) evidence. This is contrary to empirical findings. The largest increase was observed for smallest priors when presented with supporting evidence. The largest decrease was observed for highest priors when presented with conflicting evidence. Further, Bayesian theory fails to explain the 'recency' and the 'dilution' effects.
An Expert System Approach to Audit Planning and Evaluation in the Belief-Function Framework
International Journal of Intelligent Systems in Accounting, Finance & Management, 1996
No. 47 (AICPA 1983) uses a simple structure 2 of the audit evidence and treats risks as probabilities (Srivastava and Shafer 1992). However, audit evidence, in general, forms a network (see, e.g., Arens and Loebbecke 1994, Dutta and Srivastava 1992, Srivastava and Shafer 1992. In a network, one item of evidence may provide support to more than one audit objective of an account or to more than one account. For example, the confirmation of accounts receivable provides support to the existence and accuracy objectives of the account.