Applications of Belief Functions in Business Decisions: A Review

This is the author's final draft. The publisher's official version is available from: .In this paper, we review recent applications of Dempster-Shafer theory (DST) of belief functions to auditing and business decision-making. We show how DST can better map uncertainties in the application domains than Bayesian theory of probabilities. We review the applications in auditing around three practical problems that challenge the effective application of DST, namely, hierarchical evidence, versatile evidence, and statistical evidence. We review the applications in other business decisions in two loose categories: judgment under ambiguity and business model combination. Finally, we show how the theory of linear belief functions, a new extension of DST, can provide an alternative solution to a wide range of business problems

Monte-Carlo methods make Dempster-Shafer formalism feasible

One of the main obstacles to the applications of Dempster-Shafer formalism is its computational complexity. If we combine m different pieces of knowledge, then in general case we have to perform up to 2(sup m) computational steps, which for large m is infeasible. For several important cases algorithms with smaller running time were proposed. We prove, however, that if we want to compute the belief bel(Q) in any given query Q, then exponential time is inevitable. It is still inevitable, if we want to compute bel(Q) with given precision epsilon. This restriction corresponds to the natural idea that since initial masses are known only approximately, there is no sense in trying to compute bel(Q) precisely. A further idea is that there is always some doubt in the whole knowledge, so there is always a probability p(sub o) that the expert's knowledge is wrong. In view of that it is sufficient to have an algorithm that gives a correct answer a probability greater than 1-p(sub o). If we use the original Dempster's combination rule, this possibility diminishes the running time, but still leaves the problem infeasible in the general case. We show that for the alternative combination rules proposed by Smets and Yager feasible methods exist. We also show how these methods can be parallelized, and what parallelization model fits this problem best

Rapid Diagnostic Algorithms as a Screening Tool for Tuberculosis: An Assessor Blinded Cross-Sectional Study

Background: A major obstacle to effectively treat and control tuberculosis is the absence of an accurate, rapid, and low-cost diagnostic tool. A new approach for the screening of patients for tuberculosis is the use of rapid diagnostic classification algorithms. Methods: We tested a previously published diagnostic algorithm based on four biomarkers as a screening tool for tuberculosis in a Central European patient population using an assessor-blinded cross-sectional study design. In addition, we developed an improved diagnostic classification algorithm based on a study population at a tertiary hospital in Vienna, Austria, by supervised computational statistics. Results: The diagnostic accuracy of the previously published diagnostic algorithm for our patient population consisting of 206 patients was 54% (CI: 47%–61%). An improved model was constructed using inflammation parameters and clinical information. A diagnostic accuracy of 86% (CI: 80%–90%) was demonstrated by 10-fold cross validation. An alternative model relying solely on clinical parameters exhibited a diagnostic accuracy of 85% (CI: 79%–89%). Conclusion: Here we show that a rapid diagnostic algorithm based on clinical parameters is only slightly improved by inclusion of inflammation markers in our cohort. Our results also emphasize the need for validation of new diagnostic algorithms in different settings and patient populations