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

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 ? 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 ? . 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.

SUBMITTER: Martel-Escobar M

PROVIDER: S-EPMC7512506 | biostudies-literature | 2018 Dec

REPOSITORIES: biostudies-literature

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

Martel-Escobar María M Vázquez-Polo Francisco-José FJ Hernández-Bastida Agustín A

Entropy (Basel, Switzerland) 20181201 12

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 <i>materiality</i> 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 ...[more]

PMID: 33266643

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Project description:BackgroundAfrican trypanosomiasis is a tsetse-borne parasitic infection that affects humans, wildlife, and domesticated animals. Tsetse flies are endemic to much of Sub-Saharan Africa and a spatial and temporal understanding of tsetse habitat can aid surveillance and support disease risk management. Problematically, current fine spatial resolution remote sensing data are delivered with a temporal lag and are relatively coarse temporal resolution (e.g., 16 days), which results in disease control models often targeting incorrect places. The goal of this study was to devise a heuristic for identifying tsetse habitat (at a fine spatial resolution) into the future and in the temporal gaps where remote sensing and proximal data fail to supply information.MethodsThis paper introduces a generalizable and scalable open-access version of the tsetse ecological distribution (TED) model used to predict tsetse distributions across space and time, and contributes a geospatial Bayesian Maximum Entropy (BME) prediction model trained by TED output data to forecast where, herein the Morsitans group of tsetse, persist in Kenya, a method that mitigates the temporal lag problem. This model facilitates identification of tsetse habitat and provides critical information to control tsetse, mitigate the impact of trypanosomiasis on vulnerable human and animal populations, and guide disease minimization in places with ephemeral tsetse. Moreover, this BME analysis is one of the first to utilize cluster and parallel computing along with a Monte Carlo analysis to optimize BME computations. This allows for the analysis of an exceptionally large dataset (over 2 billion data points) at a finer resolution and larger spatiotemporal scale than what had previously been possible.ResultsUnder the most conservative assessment for Kenya, the BME kriging analysis showed an overall prediction accuracy of 74.8% (limited to the maximum suitability extent). In predicting tsetse distribution outcomes for the entire country the BME kriging analysis was 97% accurate in its forecasts.ConclusionsThis work offers a solution to the persistent temporal data gap in accurate and spatially precise rainfall predictions and the delayed processing of remotely sensed data collectively in the - 45 days past to + 180 days future temporal window. As is shown here, the BME model is a reliable alternative for forecasting future tsetse distributions to allow preplanning for tsetse control. Furthermore, this model provides guidance on disease control that would otherwise not be available. These 'big data' BME methods are particularly useful for large domain studies. Considering that past BME studies required reduction of the spatiotemporal grid to facilitate analysis. Both the GEE-TED and the BME libraries have been made open source to enable reproducibility and offer continual updates into the future as new remotely sensed data become available.

Dataset Information

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

Publications

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

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