Bayesian approach for inconsistent information

authored by: M. Stein, M. Beer, V. Kreinovich
Abstract: In engineering situations, we usually have a large amount of prior knowledge that needs to be taken into account when processing data. Traditionally, the Bayesian approach is used to process data in the presence of prior knowledge. Sometimes, when we apply the traditional Bayesian techniques to engineering data, we get inconsistencies between the data and prior knowledge. These inconsistencies are usually caused by the fact that in the traditional approach, we assume that we know the exact sample values, that the prior distribution is exactly known, etc. In reality, the data is imprecise due to measurement errors, the prior knowledge is only approximately known, etc. So, a natural way to deal with the seemingly inconsistent information is to take this imprecision into account in the Bayesian approach - e.g., by using fuzzy techniques. In this paper, we describe several possible scenarios for fuzzifying the Bayesian approach. Particular attention is paid to the interaction between the estimated imprecise parameters. In this paper, to implement the corresponding fuzzy versions of the Bayesian formulas, we use straightforward computations of the related expression - which makes our computations reasonably time-consuming. Computations in the traditional (non-fuzzy) Bayesian approach are much faster - because they use algorithmically efficient reformulations of the Bayesian formulas. We expect that similar reformulations of the fuzzy Bayesian formulas will also drastically decrease the computation time and thus, enhance the practical use of the proposed methods.
External Organisation(s): University of Liverpool
University of Texas at El Paso
Bechtel OG&C Offshore
Type: Article
Journal: Information Sciences
Volume: 245
Pages: 96-111
No. of pages: 16
ISSN: 0020-0255
Publication date: 01.10.2013
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Software, Control and Systems Engineering, Theoretical Computer Science, Computer Science Applications, Information Systems and Management, Artificial Intelligence
Electronic version(s): https://europepmc.org/article/PMC/3786189 (Access: Open)
https://doi.org/10.1016/j.ins.2013.02.024 (Access: Closed)