@misc{10481/55546,
year = {2018},
month = {12},
url = {http://hdl.handle.net/10481/55546},
abstract = {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 q 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 q. 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.},
organization = {This research was partially funded by MINECO, Spain (grant number EC02017–85577–P).},
publisher = {MDPI},
keywords = {Auditing},
keywords = {Bayesian inference},
keywords = {Dollar unit sampling},
keywords = {Modified likelihood},
keywords = {Partial prior information},
title = {Bayesian Inference in Auditing with Partial Prior Information Using Maximum Entropy Priors},
author = {Martel-Escobar, María del Carmen and Vázquez-Polo, Francisco-José and Hernández-Bastida, Agustín},
}