Details
| Original language | English |
|---|---|
| Pages (from-to) | 96-111 |
| Number of pages | 16 |
| Journal | Information Sciences |
| Volume | 245 |
| Early online date | 26 Feb 2013 |
| Publication status | Published - 1 Oct 2013 |
| Externally published | Yes |
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.
Keywords
- Fuzzy random variable, Fuzzy-Bayes, Imprecise data, Imprecise probability, Uncertainty quantification
ASJC Scopus subject areas
- Computer Science(all)
- Software
- Engineering(all)
- Control and Systems Engineering
- Mathematics(all)
- Theoretical Computer Science
- Computer Science(all)
- Computer Science Applications
- Decision Sciences(all)
- Information Systems and Management
- Computer Science(all)
- Artificial Intelligence
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In: Information Sciences, Vol. 245, 01.10.2013, p. 96-111.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Bayesian approach for inconsistent information
AU - Stein, M.
AU - Beer, M.
AU - Kreinovich, V.
N1 - Funding Information: The authors gratefully acknowledge the financial support by National University of Singapore through the Ministry of Education Academic Research Fund , Grant No. R246000234133 , by the US National Science Foundation Grants HRD-0734825 (Cyber-ShARE Center of Excellence) and DUE-0926721 , by the US Grant 1 T36 GM078000-01 from the National Institutes of Health , and by a grant on from the US Office of Naval Research .
PY - 2013/10/1
Y1 - 2013/10/1
N2 - 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.
AB - 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.
KW - Fuzzy random variable
KW - Fuzzy-Bayes
KW - Imprecise data
KW - Imprecise probability
KW - Uncertainty quantification
UR - http://www.scopus.com/inward/record.url?scp=84880305543&partnerID=8YFLogxK
U2 - 10.1016/j.ins.2013.02.024
DO - 10.1016/j.ins.2013.02.024
M3 - Article
AN - SCOPUS:84880305543
VL - 245
SP - 96
EP - 111
JO - Information Sciences
JF - Information Sciences
SN - 0020-0255
ER -